. . . . . . "\u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u043F\u0442\u0438\u043C\u0438\u0437\u0430\u0446\u0438\u0438 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u043A\u0435\u0440\u0430 (\u0430\u043D\u0433\u043B. Karush \u2014 Kuhn \u2014 Tucker conditions, KKT) \u2014 \u043D\u0435\u043E\u0431\u0445\u043E\u0434\u0438\u043C\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0437\u0430\u0434\u0430\u0447\u0438 \u043D\u0435\u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u043C\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F. \u0427\u0442\u043E\u0431\u044B \u0440\u0435\u0448\u0435\u043D\u0438\u0435 \u0431\u044B\u043B\u043E \u043E\u043F\u0442\u0438\u043C\u0430\u043B\u044C\u043D\u044B\u043C, \u0434\u043E\u043B\u0436\u043D\u044B \u0431\u044B\u0442\u044C \u0432\u044B\u043F\u043E\u043B\u043D\u0435\u043D\u044B \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u043D\u043E\u0441\u0442\u0438. \u041C\u0435\u0442\u043E\u0434 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043C\u0435\u0442\u043E\u0434\u0430 \u043C\u043D\u043E\u0436\u0438\u0442\u0435\u043B\u0435\u0439 \u041B\u0430\u0433\u0440\u0430\u043D\u0436\u0430. \u0412 \u043E\u0442\u043B\u0438\u0447\u0438\u0435 \u043E\u0442 \u043D\u0435\u0433\u043E, \u043E\u0433\u0440\u0430\u043D\u0438\u0447\u0435\u043D\u0438\u044F, \u043D\u0430\u043A\u043B\u0430\u0434\u044B\u0432\u0430\u0435\u043C\u044B\u0435 \u043D\u0430 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0435, \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0442 \u0441\u043E\u0431\u043E\u0439 \u043D\u0435 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F, \u0430 \u043D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0430."@ru . "Las condiciones de Karush-Kuhn-Tucker (tambi\u00E9n conocidas como las condiciones KKT o Kuhn-Tucker) son requerimientos necesarios y suficientes para que la soluci\u00F3n de un problema de programaci\u00F3n matem\u00E1tica sea \u00F3ptima. Es una generalizaci\u00F3n del m\u00E9todo de los multiplicadores de Lagrange."@es . "Die Karush-Kuhn-Tucker-Bedingungen sind ein notwendiges Optimalit\u00E4tskriterium erster Ordnung in der nichtlinearen Optimierung. Sie sind die Verallgemeinerung der notwendigen Bedingung von Optimierungsproblemen ohne Nebenbedingungen und der Lagrange-Multiplikatoren von Optimierungsproblemen unter Gleichungsnebenbedingungen. Sie wurden zum ersten Mal 1939 in der allerdings unver\u00F6ffentlichten Master-Arbeit von William Karush aufgef\u00FChrt. Bekannter wurden diese jedoch erst 1951 nach einem Konferenz-Paper von Harold W. Kuhn und Albert W. Tucker."@de . "En programaci\u00F3 no lineal les condicions de Karush-Kuhn-Tucker (tamb\u00E9 anomenades condicions de KKT, o condicions Kuhn-Tucker) s\u00F3n condicions que ha de complir un punt que sigui soluci\u00F3 d'un problema de la forma: on on On, si definim i : Es tracta d'una generalitzaci\u00F3 del M\u00E8tode dels multiplicadors de Lagrange."@ca . . "Condi\u00E7\u00F5es de Karush-Kuhn-Tucker"@pt . "\u0641\u064A \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u060C \u062A\u0639\u062A\u0628\u0631 \u0634\u0631\u0648\u0637 \u0643\u0627\u0631\u0648\u0634 \u0643\u0648\u0647\u0646 \u062A\u0627\u0643\u0631 (KKT)\u060C \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0623\u064A\u0636\u0627 \u0628\u0627\u0633\u0645 \u0634\u0631\u0648\u0637 \u0643\u0648\u0647\u0646 \u062A\u0627\u0643\u0631\u060C \u0647\u064A \u0627\u062E\u062A\u0628\u0627\u0631\u0627\u062A \u0645\u0634\u062A\u0642\u0629 \u0623\u0648\u0644\u0649 (\u062A\u0633\u0645\u0649 \u0623\u062D\u064A\u0627\u0646\u0627 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0636\u0631\u0648\u0631\u064A\u0629 \u0645\u0646 \u0627\u0644\u062F\u0631\u062C\u0629 \u0627\u0644\u0623\u0648\u0644\u0649) \u0644\u0625\u064A\u062C\u0627\u062F \u062D\u0644 \u0641\u064A \u0627\u0644\u0628\u0631\u0645\u062C\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u064A\u0643\u0648\u0646 \u0647\u0648 \u0627\u0644\u0623\u0645\u062B\u0644\u060C \u0634\u0631\u064A\u0637\u0629 \u0627\u0633\u062A\u064A\u0641\u0627\u0621 \u0628\u0639\u0636 \u0634\u0631\u0648\u0637 \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0648\u0627\u0644\u0633\u0645\u0627\u062D \u0628\u0642\u064A\u0648\u062F \u0639\u062F\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u0641\u0631\u0648\u0636\u0629 \u0639\u0644\u0649 \u062F\u0627\u0644\u0629 \u0627\u0644\u0647\u062F\u0641\u060C \u0641\u0625\u0646 \u0646\u0647\u062C KKT \u0641\u064A \u0627\u0644\u0628\u0631\u0645\u062C\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u064A\u0639\u0645\u0645 \u0637\u0631\u064A\u0642\u0629 \u0645\u0636\u0627\u0639\u0641\u0627\u062A \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u0627\u0644\u062A\u064A \u0644\u0627 \u062A\u0633\u0645\u062D \u0641\u064A \u0627\u0644\u0623\u0635\u0644 \u0625\u0644\u0627 \u0628\u0642\u064A\u0648\u062F \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629. \u0639\u0644\u0649 \u063A\u0631\u0627\u0631 \u0646\u0647\u062C \u0644\u0627\u062C\u0631\u0627\u0646\u062C\u060C \u062A\u062A\u0645 \u0625\u0639\u0627\u062F\u0629 \u0635\u064A\u0627\u063A\u0629 \u0645\u0634\u0643\u0644\u0629 \u0625\u064A\u062C\u0627\u062F \u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 \u0627\u0644\u0645\u0642\u064A\u062F\u0629 (\u0627\u0644\u062A\u0635\u063A\u064A\u0631) \u0643\u062F\u0627\u0644\u0629 \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u0627\u0644\u062A\u064A \u062A\u0643\u0648\u0646 \u0646\u0642\u0637\u062A\u0647\u0627 \u0627\u0644\u0645\u062B\u0644\u0649 \u0647\u064A \u0646\u0642\u0637\u0629 \u0627\u0644\u0633\u0631\u062C \u062A\u0644\u0639\u0628 \u0647\u0630\u0647 \u0627\u0644\u0638\u0631\u0648\u0641 \u062F\u0648\u0631\u0627 \u0645\u0647\u0645\u0627 \u062C\u062F\u0627 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u0627\u0644\u0645\u0642\u064A\u062F\u0629 \u0648\u062A\u0637\u0648\u064A\u0631 \u0627\u0644\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629. \u0644\u0644\u062D\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0634\u0643\u0644\u0629 \u0625\u0633\u062A\u0645\u062B\u0627\u0644:"@ar . . . . "\u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u043F\u0442\u0438\u043C\u0438\u0437\u0430\u0446\u0438\u0438 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u043A\u0435\u0440\u0430 (\u0430\u043D\u0433\u043B. Karush \u2014 Kuhn \u2014 Tucker conditions, KKT) \u2014 \u043D\u0435\u043E\u0431\u0445\u043E\u0434\u0438\u043C\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0437\u0430\u0434\u0430\u0447\u0438 \u043D\u0435\u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u043C\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F. \u0427\u0442\u043E\u0431\u044B \u0440\u0435\u0448\u0435\u043D\u0438\u0435 \u0431\u044B\u043B\u043E \u043E\u043F\u0442\u0438\u043C\u0430\u043B\u044C\u043D\u044B\u043C, \u0434\u043E\u043B\u0436\u043D\u044B \u0431\u044B\u0442\u044C \u0432\u044B\u043F\u043E\u043B\u043D\u0435\u043D\u044B \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u043D\u043E\u0441\u0442\u0438. \u041C\u0435\u0442\u043E\u0434 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043C\u0435\u0442\u043E\u0434\u0430 \u043C\u043D\u043E\u0436\u0438\u0442\u0435\u043B\u0435\u0439 \u041B\u0430\u0433\u0440\u0430\u043D\u0436\u0430. \u0412 \u043E\u0442\u043B\u0438\u0447\u0438\u0435 \u043E\u0442 \u043D\u0435\u0433\u043E, \u043E\u0433\u0440\u0430\u043D\u0438\u0447\u0435\u043D\u0438\u044F, \u043D\u0430\u043A\u043B\u0430\u0434\u044B\u0432\u0430\u0435\u043C\u044B\u0435 \u043D\u0430 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0435, \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0442 \u0441\u043E\u0431\u043E\u0439 \u043D\u0435 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F, \u0430 \u043D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0430."@ru . "Em otimiza\u00E7\u00E3o, as Condi\u00E7\u00F5es de Karush-Kuhn-Tucker (tamb\u00E9m conhecidas como Condi\u00E7\u00F5es de Kuhn-Tucker ou condi\u00E7\u00F5es KKT) s\u00E3o condi\u00E7\u00F5es de primeira ordem para que uma solu\u00E7\u00E3o de um problema de programa\u00E7\u00E3o n\u00E3o linear seja \u00F3tima, desde que valham condi\u00E7\u00F5es chamadas de condi\u00E7\u00F5es de qualifica\u00E7\u00E3o ou, em ingl\u00EAs, constraint qualifications. Permitindo restri\u00E7\u00F5es de desigualdade, as condi\u00E7\u00F5es KKT generalizam, na programa\u00E7\u00E3o n\u00E3o linear, o m\u00E9todo de multiplicadores de Lagrange, que permite somente restri\u00E7\u00F5es de igualdade. O sistema de equa\u00E7\u00F5es e inequa\u00E7\u00F5es correspondente \u00E0s condi\u00E7\u00F5es KKT em geral n\u00E3o \u00E9 resolvido diretamente, exceto em alguns casos especiais onde uma solu\u00E7\u00E3o pode ser obtida analiticamente. Nos demais casos, diversos algoritmos de otimiza\u00E7\u00E3o podem ser usados para resolver numericamente o sistema. As condi\u00E7\u00F5es KKT foram originalmente nomeadas ap\u00F3s Harold W. Kuhn e Albert W. Tucker, que primeiro publicaram essas condi\u00E7\u00F5es em 1951. Por\u00E9m, estudiosos posteriores descobriram que as condi\u00E7\u00F5es necess\u00E1rias para esse problema j\u00E1 haviam sido ditadas por em sua tese de mestrado em 1939."@pt . . . . . . . . . "\u30AB\u30EB\u30FC\u30B7\u30E5\u30FB\u30AF\u30FC\u30F3\u30FB\u30BF\u30C3\u30AB\u30FC\u6761\u4EF6\uFF08\u82F1: Karush-Kuhn-Tucker condition\uFF09\u3042\u308B\u3044\u306FKKT\u6761\u4EF6\u3068\u306F\u3001\u975E\u7DDA\u5F62\u8A08\u753B\u306B\u304A\u3044\u3066\u4E00\u968E\u5C0E\u95A2\u6570\u304C\u6E80\u305F\u3059\u3079\u304D\u6700\u9069\u6761\u4EF6\u3092\u6307\u3059\u3002\u30E9\u30B0\u30E9\u30F3\u30B8\u30E5\u306E\u672A\u5B9A\u4E57\u6570\u6CD5\u304C\u7B49\u5F0F\u5236\u7D04\u306E\u307F\u3092\u6271\u3046\u306E\u306B\u5BFE\u3057\u3066\u3001KKT\u6761\u4EF6\u3092\u7528\u3044\u305F\u89E3\u6CD5\u306F\u4E0D\u7B49\u5F0F\u5236\u7D04\u3082\u6271\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u3002KKT\u6761\u4EF6\u306B\u5BFE\u5FDC\u3059\u308B\u9023\u7ACB\u65B9\u7A0B\u5F0F\u306F\u3001\u89E3\u6790\u7684\u306B\u9589\u5F62\u5F0F\u89E3\u6CD5\u304C\u5C0E\u304B\u308C\u308B\u7279\u6B8A\u306A\u5834\u5408\u3092\u9664\u3044\u3066\u306F\u76F4\u63A5\u7684\u306B\u306F\u89E3\u304B\u306A\u3044\u3002\u3059\u3067\u306BKKT\u6761\u4EF6\u306E\u9023\u7ACB\u65B9\u7A0B\u5F0F\u3092\u6570\u5024\u7684\u306B\u89E3\u304F\u65B9\u6CD5\u306F\u6570\u591A\u304F\u78BA\u7ACB\u3055\u308C\u3066\u304A\u308A\u3001\u305D\u308C\u3089\u3092\u7528\u3044\u3066\u89E3\u304F\u306E\u304C\u4E00\u822C\u7684\u3067\u3042\u308B\u3002KKT\u6761\u4EF6\u306F\u7DDA\u5F62\u8A08\u753B\u6CD5\u306B\u304A\u3051\u308B\u4E3B\u53CC\u5BFE\u5185\u70B9\u6CD5\u306A\u3069\u306E\u89E3\u6CD5\u306B\u304A\u3044\u3066\u3001\u91CD\u8981\u306A\u5F79\u5272\u3092\u6301\u3064\u3002"@ja . . . . . . . . . . . "\u0641\u064A \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u060C \u062A\u0639\u062A\u0628\u0631 \u0634\u0631\u0648\u0637 \u0643\u0627\u0631\u0648\u0634 \u0643\u0648\u0647\u0646 \u062A\u0627\u0643\u0631 (KKT)\u060C \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0623\u064A\u0636\u0627 \u0628\u0627\u0633\u0645 \u0634\u0631\u0648\u0637 \u0643\u0648\u0647\u0646 \u062A\u0627\u0643\u0631\u060C \u0647\u064A \u0627\u062E\u062A\u0628\u0627\u0631\u0627\u062A \u0645\u0634\u062A\u0642\u0629 \u0623\u0648\u0644\u0649 (\u062A\u0633\u0645\u0649 \u0623\u062D\u064A\u0627\u0646\u0627 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0636\u0631\u0648\u0631\u064A\u0629 \u0645\u0646 \u0627\u0644\u062F\u0631\u062C\u0629 \u0627\u0644\u0623\u0648\u0644\u0649) \u0644\u0625\u064A\u062C\u0627\u062F \u062D\u0644 \u0641\u064A \u0627\u0644\u0628\u0631\u0645\u062C\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u064A\u0643\u0648\u0646 \u0647\u0648 \u0627\u0644\u0623\u0645\u062B\u0644\u060C \u0634\u0631\u064A\u0637\u0629 \u0627\u0633\u062A\u064A\u0641\u0627\u0621 \u0628\u0639\u0636 \u0634\u0631\u0648\u0637 \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0648\u0627\u0644\u0633\u0645\u0627\u062D \u0628\u0642\u064A\u0648\u062F \u0639\u062F\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u0641\u0631\u0648\u0636\u0629 \u0639\u0644\u0649 \u062F\u0627\u0644\u0629 \u0627\u0644\u0647\u062F\u0641\u060C \u0641\u0625\u0646 \u0646\u0647\u062C KKT \u0641\u064A \u0627\u0644\u0628\u0631\u0645\u062C\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u064A\u0639\u0645\u0645 \u0637\u0631\u064A\u0642\u0629 \u0645\u0636\u0627\u0639\u0641\u0627\u062A \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u0627\u0644\u062A\u064A \u0644\u0627 \u062A\u0633\u0645\u062D \u0641\u064A \u0627\u0644\u0623\u0635\u0644 \u0625\u0644\u0627 \u0628\u0642\u064A\u0648\u062F \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629. \u0639\u0644\u0649 \u063A\u0631\u0627\u0631 \u0646\u0647\u062C \u0644\u0627\u062C\u0631\u0627\u0646\u062C\u060C \u062A\u062A\u0645 \u0625\u0639\u0627\u062F\u0629 \u0635\u064A\u0627\u063A\u0629 \u0645\u0634\u0643\u0644\u0629 \u0625\u064A\u062C\u0627\u062F \u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 \u0627\u0644\u0645\u0642\u064A\u062F\u0629 (\u0627\u0644\u062A\u0635\u063A\u064A\u0631) \u0643\u062F\u0627\u0644\u0629 \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u0627\u0644\u062A\u064A \u062A\u0643\u0648\u0646 \u0646\u0642\u0637\u062A\u0647\u0627 \u0627\u0644\u0645\u062B\u0644\u0649 \u0647\u064A \u0646\u0642\u0637\u0629 \u0627\u0644\u0633\u0631\u062C \u062A\u0644\u0639\u0628 \u0647\u0630\u0647 \u0627\u0644\u0638\u0631\u0648\u0641 \u062F\u0648\u0631\u0627 \u0645\u0647\u0645\u0627 \u062C\u062F\u0627 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u0627\u0644\u0645\u0642\u064A\u062F\u0629 \u0648\u062A\u0637\u0648\u064A\u0631 \u0627\u0644\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629. \u0644\u0644\u062D\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0634\u0643\u0644\u0629 \u0625\u0633\u062A\u0645\u062B\u0627\u0644: min\u2061 f(x) \u062A\u062E\u0636\u0639 \u0625\u0644\u0649 gi(x) - bi \u2265 0 , i=1,\u2026,k gi(x) - bi = 0 , i=k+1,\u2026,m \u0647\u0646\u0627\u0643 \u0623\u0631\u0628\u0639\u0629 \u0634\u0631\u0648\u0637 KKT \u0644\u0628\u062F\u0627\u064A\u0629 \u0645\u062B\u0644\u0649 : 1. \u0627\u0644\u0642\u064A\u0648\u062F \u0627\u0644\u0645\u062C\u062F\u064A\u0629:gi(x*) - bi 2. \u0644\u0627 \u064A\u0648\u062C\u062F \u0647\u0628\u0648\u0637 \u0645\u0645\u0643\u0646:f(x*) - \u03A3i=1,m \u03BBi* \u2207gi(x*) = 0\u2207 3. \u0627\u0644\u0631\u0643\u0648\u062F \u0627\u0644\u062A\u0643\u0645\u064A\u0644\u064A:\u03BBi*(gi(x*) - bi) = 0 4. \u0645\u0636\u0627\u0639\u0641\u0627\u062A \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u0625\u064A\u062C\u0627\u0628\u064A\u0629:\u03BBi* \u2265 0 \u064A\u0634\u064A\u0631 \u0631\u0645\u0632 \u0627\u0644\u0646\u062C\u0645\u0629 (*) \u0625\u0644\u0649 \u0627\u0644\u0642\u064A\u0645 \u0627\u0644\u0645\u062B\u0644\u0649. \u064A\u0646\u0637\u0628\u0642 \u0634\u0631\u0637 \u0627\u0644\u062C\u062F\u0648\u0649 (1) \u0639\u0644\u0649 \u0643\u0644 \u0645\u0646 \u0642\u064A\u0648\u062F \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0648\u0639\u062F\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629\u060C \u0628\u0645\u062C\u0631\u062F \u0625\u062B\u0628\u0644\u062A \u0646\u0647 \u064A\u062C\u0628 \u0639\u062F\u0645 \u0627\u0646\u062A\u0647\u0627\u0643 \u0627\u0644\u0642\u064A\u0648\u062F \u0641\u064A \u0627\u0644\u0638\u0631\u0648\u0641 \u0627\u0644\u0645\u062B\u0644\u0649.\u0634\u0631\u0637 \u0627\u0644\u062A\u062F\u0631\u062C (2) \u064A\u0636\u0645\u0646 \u0639\u062F\u0645 \u0648\u062C\u0648\u062F \u0627\u062A\u062C\u0627\u0647 \u0645\u0645\u0643\u0646 \u064A\u0645\u0643\u0646 \u0623\u0646 \u064A\u062D\u0633\u0646 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0647\u062F\u0641.\u0627\u0644\u0634\u0631\u0637\u064A\u0646 \u0627\u0644\u0623\u062E\u064A\u0631\u064A\u0646 (3 \u0648 4) \u0645\u0637\u0644\u0648\u0628\u064A\u0646 \u0641\u064A \u062D\u0627\u0644\u0629 \u0648\u062C\u0648\u062F \u0642\u064A\u0648\u062F \u0639\u062F\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0648\u0623\u0646 \u0645\u0636\u0627\u0639\u0641\u0627\u062A \u0644\u0627\u062C\u0631\u0627\u0646\u062C \u062A\u0643\u0648\u0646 \u0645\u0648\u062C\u0628\u0629 \u0641\u064A \u062D\u0627\u0644\u0629 \u0627\u0644\u0642\u064A\u062F \u0627\u0644\u0646\u0634\u0637 (=0) \u0648\u062A\u0633\u0627\u0648\u064A \u0635\u0641\u0631 \u0641\u064A \u062D\u0627\u0644\u0629 \u0627\u0644\u0642\u064A\u062F \u0627\u0644\u063A\u064A\u0631 \u0646\u0634\u0637 (>0). \u062A\u0634\u0643\u0644 \u0634\u0631\u0648\u0637 KKT (Karush-Kuhn-Tucker) \u0627\u0644\u0639\u0645\u0648\u062F \u0627\u0644\u0641\u0642\u0631\u064A \u0644\u0644\u0628\u0631\u0645\u062C\u0629 \u0627\u0644\u062E\u0637\u064A\u0629 \u0648\u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u0641\u062A\u0645\u062B\u0644 \u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u0646\u0638\u0631\u064A\u0629 \u0644\u0644\u0639\u062F\u064A\u062F \u0645\u0646 \u0627\u0644\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0627\u062A\u060C \u0646\u0630\u0643\u0631 \u0645\u0646\u0647\u0627 \u0639\u0644\u0649 \u0648\u062C\u0647 \u0627\u0644\u062E\u0635\u0648\u0635 \u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629 \u0643\u0627\u0631\u0645\u0627\u0631\u0643\u0631 \u0648\u0637\u0631\u064A\u0642\u0629 \u0627\u0644\u0633\u064A\u0645\u0628\u0644\u0643\u0633. \u0643\u0645\u0627 \u0647\u064A: \n* \u0636\u0631\u0648\u0631\u064A\u0629 \u0648\u0643\u0627\u0641\u064A\u0629 \u0644\u062A\u062D\u0642\u064A\u0642 \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u0641\u064A \u0627\u0644\u0628\u0631\u0645\u062C\u0629 \u0627\u0644\u062E\u0637\u064A\u0629. \n* \u0636\u0631\u0648\u0631\u064A\u0629 \u0648\u0643\u0627\u0641\u064A\u0629 \u0644\u062A\u062D\u0642\u064A\u0642 \u0627\u0644\u0623\u0645\u062B\u0644\u064A\u0629 \u0627\u0644\u0645\u062D\u062F\u0628\u0629\u060C \u0645\u062B\u0644 \u062A\u0635\u063A\u064A\u0631 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0623\u0642\u0644 \u0641\u064A \u0627\u0644\u0627\u0646\u062D\u062F\u0627\u0631 \u0627\u0644\u062E\u0637\u064A. \n* \u0636\u0631\u0648\u0631\u064A\u0629 \u0644\u062A\u062D\u0642\u064A\u0642 \u0627\u0644\u0623\u0645\u062B\u0644 \u0641\u064A \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0625\u0633\u062A\u0645\u062B\u0627\u0644 \u063A\u064A\u0631 \u0627\u0644\u0645\u062D\u062F\u0628\u0629\u060C \u0645\u062B\u0644 \u062A\u062F\u0631\u064A\u0628 \u0646\u0645\u0648\u0630\u062C \u0627\u0644\u062A\u0639\u0644\u0645 \u0627\u0644\u0639\u0645\u064A\u0642."@ar . "\uCE74\uB8E8\uC2DC-\uCFE4-\uD130\uCEE4 \uC870\uAC74"@ko . "\u30AB\u30EB\u30FC\u30B7\u30E5\u30FB\u30AF\u30FC\u30F3\u30FB\u30BF\u30C3\u30AB\u30FC\u6761\u4EF6\uFF08\u82F1: Karush-Kuhn-Tucker condition\uFF09\u3042\u308B\u3044\u306FKKT\u6761\u4EF6\u3068\u306F\u3001\u975E\u7DDA\u5F62\u8A08\u753B\u306B\u304A\u3044\u3066\u4E00\u968E\u5C0E\u95A2\u6570\u304C\u6E80\u305F\u3059\u3079\u304D\u6700\u9069\u6761\u4EF6\u3092\u6307\u3059\u3002\u30E9\u30B0\u30E9\u30F3\u30B8\u30E5\u306E\u672A\u5B9A\u4E57\u6570\u6CD5\u304C\u7B49\u5F0F\u5236\u7D04\u306E\u307F\u3092\u6271\u3046\u306E\u306B\u5BFE\u3057\u3066\u3001KKT\u6761\u4EF6\u3092\u7528\u3044\u305F\u89E3\u6CD5\u306F\u4E0D\u7B49\u5F0F\u5236\u7D04\u3082\u6271\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u3002KKT\u6761\u4EF6\u306B\u5BFE\u5FDC\u3059\u308B\u9023\u7ACB\u65B9\u7A0B\u5F0F\u306F\u3001\u89E3\u6790\u7684\u306B\u9589\u5F62\u5F0F\u89E3\u6CD5\u304C\u5C0E\u304B\u308C\u308B\u7279\u6B8A\u306A\u5834\u5408\u3092\u9664\u3044\u3066\u306F\u76F4\u63A5\u7684\u306B\u306F\u89E3\u304B\u306A\u3044\u3002\u3059\u3067\u306BKKT\u6761\u4EF6\u306E\u9023\u7ACB\u65B9\u7A0B\u5F0F\u3092\u6570\u5024\u7684\u306B\u89E3\u304F\u65B9\u6CD5\u306F\u6570\u591A\u304F\u78BA\u7ACB\u3055\u308C\u3066\u304A\u308A\u3001\u305D\u308C\u3089\u3092\u7528\u3044\u3066\u89E3\u304F\u306E\u304C\u4E00\u822C\u7684\u3067\u3042\u308B\u3002KKT\u6761\u4EF6\u306F\u7DDA\u5F62\u8A08\u753B\u6CD5\u306B\u304A\u3051\u308B\u4E3B\u53CC\u5BFE\u5185\u70B9\u6CD5\u306A\u3069\u306E\u89E3\u6CD5\u306B\u304A\u3044\u3066\u3001\u91CD\u8981\u306A\u5F79\u5272\u3092\u6301\u3064\u3002"@ja . . . . "\u0423\u043C\u043E\u0432\u0438 \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u0435\u0440\u0430"@uk . "\u30AB\u30EB\u30FC\u30B7\u30E5\u30FB\u30AF\u30FC\u30F3\u30FB\u30BF\u30C3\u30AB\u30FC\u6761\u4EF6"@ja . "Karush\u2013Kuhn\u2013Tucker-villkor (eller KKT-villkor) \u00E4r ett villkor som m\u00E5ste vara uppfyllt f\u00F6r att en punkt ska vara en till ett optimeringsproblem. Villkoret \u00E4r n\u00F6dv\u00E4ndigt men inte tillr\u00E4ckligt, det vill s\u00E4ga om villkoret \u00E4r uppfyllt s\u00E5 beh\u00F6ver det inte betyda att punkten \u00E4r optimum. Dock \u00E4r det s\u00E4kert att optimum uppfyller villkoret s\u00E5 en punkt som inte uppfyller villkoret kan inte vara optimum."@sv . "En math\u00E9matiques, les conditions de Karush-Kuhn-Tucker ou anciennement conditions de Kuhn-Tucker sont une g\u00E9n\u00E9ralisation des multiplicateurs de Lagrange qui permettent de r\u00E9soudre des probl\u00E8mes d'optimisation sous contraintes non lin\u00E9aires d'in\u00E9galit\u00E9s. Soit , une fonction appel\u00E9e fonction objectif, et des fonctions , , appel\u00E9es contraintes. On suppose que et les sont de classe C1. Le probl\u00E8me \u00E0 r\u00E9soudre est le suivant : Trouver qui maximise sous les contraintes pour tout ."@fr . . . . "En programaci\u00F3 no lineal les condicions de Karush-Kuhn-Tucker (tamb\u00E9 anomenades condicions de KKT, o condicions Kuhn-Tucker) s\u00F3n condicions que ha de complir un punt que sigui soluci\u00F3 d'un problema de la forma: on on On, si definim i : Es tracta d'una generalitzaci\u00F3 del M\u00E8tode dels multiplicadors de Lagrange."@ca . "\u5361\u9C81\u4EC0-\u5E93\u6069-\u5854\u514B\u6761\u4EF6"@zh . . . . . "In mathematical optimization, the Karush\u2013Kuhn\u2013Tucker (KKT) conditions, also known as the Kuhn\u2013Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some are satisfied. The KKT conditions were originally named after Harold W. Kuhn and Albert W. Tucker, who first published the conditions in 1951. Later scholars discovered that the necessary conditions for this problem had been stated by William Karush in his master's thesis in 1939."@en . . "\uCE74\uB8E8\uC2DC-\uCFE4-\uD130\uCEE4 \uC870\uAC74(Karush\u2013Kuhn\u2013Tucker conditions) \uB610\uB294 KKT \uC870\uAC74\uC740 (William Karush), (Harold W. Kuhn), (Albert W. Tucker)\uAC00 \uB9CC\uB4E0 \uCD5C\uC801\uD654\uC758 \uC870\uAC74\uC73C\uB85C \uB77C\uADF8\uB791\uC8FC \uC2B9\uC218\uBC95\uC744 \uBD80\uB4F1\uC2DD\uC744 \uAC00\uC9C4 \uACBD\uC6B0\uB85C \uC77C\uBC18\uD654\uD55C \uAC83\uC774\uB2E4."@ko . "\u0423\u043C\u043E\u0432\u0438 \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u0435\u0440\u0430 \u2014 \u043D\u0435\u043E\u0431\u0445\u0456\u0434\u043D\u0456 \u0443\u043C\u043E\u0432\u0438 \u043E\u043F\u0442\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0441\u0442\u0456 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0443 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u043D\u0435\u043B\u0456\u043D\u0456\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u043F\u0440\u0438 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u0456 \u0434\u0435\u044F\u043A\u0438\u0445 \u0443\u043C\u043E\u0432 \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u043D\u043E\u0441\u0442\u0456. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0430\u0432\u0442\u043E\u0440\u0456\u0432: \u0412\u0456\u043B\u044C\u044F\u043C\u0430 \u041A\u0430\u0440\u0443\u0448\u0430, \u0456 . \u041D\u0435\u0445\u0430\u0439 \u043C\u0430\u0454\u043C\u043E \u043D\u0430\u0441\u0442\u0443\u043F\u043D\u0443 \u0437\u0430\u0434\u0430\u0447\u0443 \u043E\u043F\u0442\u0438\u043C\u0456\u0437\u0430\u0446\u0456\u0457: \u043F\u0440\u0438 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u0456 \u0443\u043C\u043E\u0432\u0434\u0435 \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u044F, \u0449\u043E \u043C\u0456\u043D\u0456\u043C\u0456\u0437\u0443\u0454\u0442\u044C\u0441\u044F, \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u043E\u0431\u043C\u0435\u0436\u0435\u043D\u044C-\u043D\u0435\u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0435\u0439 \u0456 \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u043E\u0431\u043C\u0435\u0436\u0435\u043D\u044C-\u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0435\u0439."@uk . "Condiciones de Karush-Kuhn-Tucker"@es . . . . . . "\u0634\u0631\u0648\u0637 \u0643\u0627\u0631\u0648\u0634 \u0643\u0648\u0647\u0646 \u062A\u0627\u0643\u0631"@ar . . . "Karush\u2013Kuhn\u2013Tucker-villkor"@sv . . "En math\u00E9matiques, les conditions de Karush-Kuhn-Tucker ou anciennement conditions de Kuhn-Tucker sont une g\u00E9n\u00E9ralisation des multiplicateurs de Lagrange qui permettent de r\u00E9soudre des probl\u00E8mes d'optimisation sous contraintes non lin\u00E9aires d'in\u00E9galit\u00E9s. Soit , une fonction appel\u00E9e fonction objectif, et des fonctions , , appel\u00E9es contraintes. On suppose que et les sont de classe C1. Le probl\u00E8me \u00E0 r\u00E9soudre est le suivant : Trouver qui maximise sous les contraintes pour tout ."@fr . "Las condiciones de Karush-Kuhn-Tucker (tambi\u00E9n conocidas como las condiciones KKT o Kuhn-Tucker) son requerimientos necesarios y suficientes para que la soluci\u00F3n de un problema de programaci\u00F3n matem\u00E1tica sea \u00F3ptima. Es una generalizaci\u00F3n del m\u00E9todo de los multiplicadores de Lagrange."@es . "\u5728\u6578\u5B78\u4E2D\uFF0C\u5361\u9C81\u4EC0-\u5E93\u6069-\u5854\u514B\u6761\u4EF6\uFF08\u82F1\u6587\u539F\u540D\uFF1AKarush-Kuhn-Tucker Conditions\uFF0C\u5E38\u898B\u5225\u540D\uFF1AKuhn-Tucker\uFF0CKKT\u689D\u4EF6\uFF0CKarush-Kuhn-Tucker\u6700\u512A\u5316\u689D\u4EF6\uFF0CKarush-Kuhn-Tucker\u689D\u4EF6\uFF0CKuhn-Tucker\u6700\u512A\u5316\u689D\u4EF6\uFF0CKuhn-Tucker\u689D\u4EF6\uFF09\u662F\u5728\u6EE1\u8DB3\u4E00\u4E9B\u6709\u89C4\u5219\u7684\u6761\u4EF6\u4E0B\uFF0C\u4E00\u500B\u975E\u7DDA\u6027\u898F\u5283\uFF08Nonlinear Programming\uFF09\u554F\u984C\u80FD\u6709\u6700\u512A\u5316\u89E3\u6CD5\u7684\u4E00\u500B\u5FC5\u8981\u689D\u4EF6\u3002\u9019\u662F\u4E00\u500B\u4F7F\u7528\u5E7F\u4E49\u62C9\u683C\u6717\u65E5\u51FD\u6570\u7684\u7ED3\u679C\u3002 \u8003\u616E\u4EE5\u4E0B\u975E\u7DDA\u5F0F\u6700\u512A\u5316\u554F\u984C\uFF1A \u662F\u9700\u8981\u6700\u5C0F\u5316\u7684\u51FD\u6578\uFF0C\u662F\u4E0D\u7B49\u5F0F\u7D04\u675F\uFF0C\u662F\u7B49\u5F0F\u7D04\u675F\uFF0C\u548C\u5206\u5225\u70BA\u4E0D\u7B49\u5F0F\u7D04\u675F\u548C\u7B49\u5F0F\u7D04\u675F\u7684\u6578\u91CF\u3002 \u4E0D\u7B49\u5F0F\u7D04\u675F\u554F\u984C\u7684\u5FC5\u8981\u548C\u5145\u5206\u689D\u4EF6\u521D\u898B\u65BC\u7684\u7855\u58EB\u8AD6\u6587\uFF0C\u4E4B\u5F8C\u5728\u4E00\u4EFD\u7531W.\u5E93\u6069\uFF08Harold W. Kuhn\uFF09\u53CA\u5854\u514B\uFF08Albert W. Tucker\uFF09\u64B0\u5BEB\u7684\u7814\u7A76\u751F\u8AD6\u6587\u51FA\u73FE\u5F8C\u53D7\u5230\u91CD\u8996\u3002"@zh . . . . . . . "Condizioni di Karush-Kuhn-Tucker"@it . "\u0423\u043C\u043E\u0432\u0438 \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u0435\u0440\u0430 \u2014 \u043D\u0435\u043E\u0431\u0445\u0456\u0434\u043D\u0456 \u0443\u043C\u043E\u0432\u0438 \u043E\u043F\u0442\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0441\u0442\u0456 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0443 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u043D\u0435\u043B\u0456\u043D\u0456\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u043F\u0440\u0438 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u0456 \u0434\u0435\u044F\u043A\u0438\u0445 \u0443\u043C\u043E\u0432 \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u043D\u043E\u0441\u0442\u0456. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0430\u0432\u0442\u043E\u0440\u0456\u0432: \u0412\u0456\u043B\u044C\u044F\u043C\u0430 \u041A\u0430\u0440\u0443\u0448\u0430, \u0456 . \u041D\u0435\u0445\u0430\u0439 \u043C\u0430\u0454\u043C\u043E \u043D\u0430\u0441\u0442\u0443\u043F\u043D\u0443 \u0437\u0430\u0434\u0430\u0447\u0443 \u043E\u043F\u0442\u0438\u043C\u0456\u0437\u0430\u0446\u0456\u0457: \u043F\u0440\u0438 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u0456 \u0443\u043C\u043E\u0432\u0434\u0435 \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u044F, \u0449\u043E \u043C\u0456\u043D\u0456\u043C\u0456\u0437\u0443\u0454\u0442\u044C\u0441\u044F, \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u043E\u0431\u043C\u0435\u0436\u0435\u043D\u044C-\u043D\u0435\u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0435\u0439 \u0456 \u2014 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u043E\u0431\u043C\u0435\u0436\u0435\u043D\u044C-\u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0435\u0439."@uk . . . . "In mathematical optimization, the Karush\u2013Kuhn\u2013Tucker (KKT) conditions, also known as the Kuhn\u2013Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some are satisfied. Allowing inequality constraints, the KKT approach to nonlinear programming generalizes the method of Lagrange multipliers, which allows only equality constraints. Similar to the Lagrange approach, the constrained maximization (minimization) problem is rewritten as a Lagrange function whose optimal point is a saddle point, i.e. a global maximum (minimum) over the domain of the choice variables and a global minimum (maximum) over the multipliers, which is why the Karush\u2013Kuhn\u2013Tucker theorem is sometimes referred to as the saddle-point theorem. The KKT conditions were originally named after Harold W. Kuhn and Albert W. Tucker, who first published the conditions in 1951. Later scholars discovered that the necessary conditions for this problem had been stated by William Karush in his master's thesis in 1939."@en . . "\u0423\u0441\u043B\u043E\u0432\u0438\u044F \u041A\u0430\u0440\u0443\u0448\u0430 \u2014 \u041A\u0443\u043D\u0430 \u2014 \u0422\u0430\u043A\u043A\u0435\u0440\u0430"@ru . . . "Conditions de Karush-Kuhn-Tucker"@fr . . . . "Em otimiza\u00E7\u00E3o, as Condi\u00E7\u00F5es de Karush-Kuhn-Tucker (tamb\u00E9m conhecidas como Condi\u00E7\u00F5es de Kuhn-Tucker ou condi\u00E7\u00F5es KKT) s\u00E3o condi\u00E7\u00F5es de primeira ordem para que uma solu\u00E7\u00E3o de um problema de programa\u00E7\u00E3o n\u00E3o linear seja \u00F3tima, desde que valham condi\u00E7\u00F5es chamadas de condi\u00E7\u00F5es de qualifica\u00E7\u00E3o ou, em ingl\u00EAs, constraint qualifications. Permitindo restri\u00E7\u00F5es de desigualdade, as condi\u00E7\u00F5es KKT generalizam, na programa\u00E7\u00E3o n\u00E3o linear, o m\u00E9todo de multiplicadores de Lagrange, que permite somente restri\u00E7\u00F5es de igualdade. O sistema de equa\u00E7\u00F5es e inequa\u00E7\u00F5es correspondente \u00E0s condi\u00E7\u00F5es KKT em geral n\u00E3o \u00E9 resolvido diretamente, exceto em alguns casos especiais onde uma solu\u00E7\u00E3o pode ser obtida analiticamente. Nos demais casos, diversos algoritmos de otimiza\u00E7\u00E3o podem ser usados para resolver numericamente o si"@pt . . . "In matematica, le condizioni di Karush\u2013Kuhn\u2013Tucker (anche conosciute come condizioni di Kuhn-Tucker o condizioni KKT) sono condizioni necessarie per la soluzione di un problema di programmazione non lineare in cui i vincoli soddisfino una delle condizioni di regolarit\u00E0 dette . Si tratta di una generalizzazione del metodo dei moltiplicatori di Lagrange, applicato a problemi in cui siano presenti anche vincoli di disuguaglianza. Tali considerazioni prendono il proprio nome da , , e e sono derivate, come caso particolare in cui siano soddisfatte le condizioni di qualificazione dei vincoli, dalle ."@it . . . . . "2397362"^^ . . . "Karush\u2013Kuhn\u2013Tucker-villkor (eller KKT-villkor) \u00E4r ett villkor som m\u00E5ste vara uppfyllt f\u00F6r att en punkt ska vara en till ett optimeringsproblem. Villkoret \u00E4r n\u00F6dv\u00E4ndigt men inte tillr\u00E4ckligt, det vill s\u00E4ga om villkoret \u00E4r uppfyllt s\u00E5 beh\u00F6ver det inte betyda att punkten \u00E4r optimum. Dock \u00E4r det s\u00E4kert att optimum uppfyller villkoret s\u00E5 en punkt som inte uppfyller villkoret kan inte vara optimum."@sv . . "Karushovy\u2013Kuhnovy\u2013Tuckerovy podm\u00EDnky"@cs . "Die Karush-Kuhn-Tucker-Bedingungen sind ein notwendiges Optimalit\u00E4tskriterium erster Ordnung in der nichtlinearen Optimierung. Sie sind die Verallgemeinerung der notwendigen Bedingung von Optimierungsproblemen ohne Nebenbedingungen und der Lagrange-Multiplikatoren von Optimierungsproblemen unter Gleichungsnebenbedingungen. Sie wurden zum ersten Mal 1939 in der allerdings unver\u00F6ffentlichten Master-Arbeit von William Karush aufgef\u00FChrt. Bekannter wurden diese jedoch erst 1951 nach einem Konferenz-Paper von Harold W. Kuhn und Albert W. Tucker."@de . . . "\uCE74\uB8E8\uC2DC-\uCFE4-\uD130\uCEE4 \uC870\uAC74(Karush\u2013Kuhn\u2013Tucker conditions) \uB610\uB294 KKT \uC870\uAC74\uC740 (William Karush), (Harold W. Kuhn), (Albert W. Tucker)\uAC00 \uB9CC\uB4E0 \uCD5C\uC801\uD654\uC758 \uC870\uAC74\uC73C\uB85C \uB77C\uADF8\uB791\uC8FC \uC2B9\uC218\uBC95\uC744 \uBD80\uB4F1\uC2DD\uC744 \uAC00\uC9C4 \uACBD\uC6B0\uB85C \uC77C\uBC18\uD654\uD55C \uAC83\uC774\uB2E4."@ko . "Karush\u2013Kuhn\u2013Tucker conditions"@en . . . . "\u5728\u6578\u5B78\u4E2D\uFF0C\u5361\u9C81\u4EC0-\u5E93\u6069-\u5854\u514B\u6761\u4EF6\uFF08\u82F1\u6587\u539F\u540D\uFF1AKarush-Kuhn-Tucker Conditions\uFF0C\u5E38\u898B\u5225\u540D\uFF1AKuhn-Tucker\uFF0CKKT\u689D\u4EF6\uFF0CKarush-Kuhn-Tucker\u6700\u512A\u5316\u689D\u4EF6\uFF0CKarush-Kuhn-Tucker\u689D\u4EF6\uFF0CKuhn-Tucker\u6700\u512A\u5316\u689D\u4EF6\uFF0CKuhn-Tucker\u689D\u4EF6\uFF09\u662F\u5728\u6EE1\u8DB3\u4E00\u4E9B\u6709\u89C4\u5219\u7684\u6761\u4EF6\u4E0B\uFF0C\u4E00\u500B\u975E\u7DDA\u6027\u898F\u5283\uFF08Nonlinear Programming\uFF09\u554F\u984C\u80FD\u6709\u6700\u512A\u5316\u89E3\u6CD5\u7684\u4E00\u500B\u5FC5\u8981\u689D\u4EF6\u3002\u9019\u662F\u4E00\u500B\u4F7F\u7528\u5E7F\u4E49\u62C9\u683C\u6717\u65E5\u51FD\u6570\u7684\u7ED3\u679C\u3002 \u8003\u616E\u4EE5\u4E0B\u975E\u7DDA\u5F0F\u6700\u512A\u5316\u554F\u984C\uFF1A \u662F\u9700\u8981\u6700\u5C0F\u5316\u7684\u51FD\u6578\uFF0C\u662F\u4E0D\u7B49\u5F0F\u7D04\u675F\uFF0C\u662F\u7B49\u5F0F\u7D04\u675F\uFF0C\u548C\u5206\u5225\u70BA\u4E0D\u7B49\u5F0F\u7D04\u675F\u548C\u7B49\u5F0F\u7D04\u675F\u7684\u6578\u91CF\u3002 \u4E0D\u7B49\u5F0F\u7D04\u675F\u554F\u984C\u7684\u5FC5\u8981\u548C\u5145\u5206\u689D\u4EF6\u521D\u898B\u65BC\u7684\u7855\u58EB\u8AD6\u6587\uFF0C\u4E4B\u5F8C\u5728\u4E00\u4EFD\u7531W.\u5E93\u6069\uFF08Harold W. Kuhn\uFF09\u53CA\u5854\u514B\uFF08Albert W. Tucker\uFF09\u64B0\u5BEB\u7684\u7814\u7A76\u751F\u8AD6\u6587\u51FA\u73FE\u5F8C\u53D7\u5230\u91CD\u8996\u3002"@zh . . "1120084873"^^ . . . "26438"^^ . . . . . . "Condicions de Karush-Kuhn-Tucker"@ca . "In matematica, le condizioni di Karush\u2013Kuhn\u2013Tucker (anche conosciute come condizioni di Kuhn-Tucker o condizioni KKT) sono condizioni necessarie per la soluzione di un problema di programmazione non lineare in cui i vincoli soddisfino una delle condizioni di regolarit\u00E0 dette . Si tratta di una generalizzazione del metodo dei moltiplicatori di Lagrange, applicato a problemi in cui siano presenti anche vincoli di disuguaglianza. Tali considerazioni prendono il proprio nome da , , e e sono derivate, come caso particolare in cui siano soddisfatte le condizioni di qualificazione dei vincoli, dalle . Considerato il seguente problema di ottimizzazione non lineare: in cui \u00E8 la funzione da minimizzare (detta anche funzione obiettivo), sono i vincoli monolateri e sono i vincoli bilateri. Le condizioni necessarie per questo generico problema di ottimizzazione vincolata furono inizialmente pubblicate, nella sua tesi di laurea magistrale, da , anche se furono conosciute solamente dopo l'articolo di e .."@it . "Karush-Kuhn-Tucker-Bedingungen"@de . . . . . .