{"id":6814,"date":"2019-04-08T13:32:16","date_gmt":"2019-04-08T12:32:16","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6814"},"modified":"2022-12-03T23:02:04","modified_gmt":"2022-12-03T22:02:04","slug":"lp-origine-non-realisable","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/lp-origin-unrealizable\/","title":{"rendered":"LP: origin not feasible"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6814\" class=\"elementor elementor-6814\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-94321db elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"94321db\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-500b042\" data-id=\"500b042\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f350dac elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f350dac\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Linear programming<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column 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class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-56d75e83 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"56d75e83\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9585f0e\" data-id=\"9585f0e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3e2871b2 elementor-widget elementor-widget-text-editor\" data-id=\"3e2871b2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/lp-origin-unrealizable\/#Origine-non-realisable\" >Origin not feasible<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Origine-non-realisable\"><\/span>Origin not feasible<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The problems of which all b<sub>i<\/sub> are positive are made with Realizable Origin. It&#039;s easy to have a <a href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/simplex-method-2\/\">basic fix<\/a> and the simplex is compatible. For the problems at the origin not realizable, one initially seeks to solve the Auxiliary Problem.<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6817 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp23.png\" alt=\"non-realizable origin degenerate simplex\" width=\"259\" height=\"162\" title=\"\"><\/figure>\n<\/div>\n\n<p>In the auxiliary problem, we add an auxiliary variable x<sub>0<\/sub>. This variable is included in all the constraints. We seek to minimize its value (maximize its opposite).<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6818 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp24.png\" alt=\"non-realizable origin degenerate simplex\" width=\"343\" height=\"447\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp24.png 343w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp24-230x300.png 230w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/figure>\n<\/div>\n\n<p>The first iteration is specific, we force the auxiliary variable to enter. The pivot line is that of which the b<sub>i<\/sub> is the smallest. The following follows the classical resolution of a simplex.<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6819 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp25.png\" alt=\"non-realizable origin degenerate simplex\" width=\"386\" height=\"519\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp25.png 386w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp25-223x300.png 223w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/figure>\n<\/div>\n\n<p>Once the simplex is optimal, we express z as a function of the non-base variables. The origin of the base variables is then achievable (here the blue boxes show the evolution of the stresses by the resolution of the simplex).<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6820 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp26.png\" alt=\"non-realizable origin degenerate simplex\" width=\"649\" height=\"291\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp26.png 649w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp26-300x135.png 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><\/figure>\n<\/div>\n\n<p>The new problem to be solved is as follows:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6821 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp27.png\" alt=\"non-realizable origin degenerate simplex\" width=\"649\" height=\"214\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp27.png 649w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp27-300x99.png 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><\/figure>\n<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Linear Programming Homepage Wiki Non-Realizable Origin Problems with all bi positive are done with Realizable Origin. It&#039;s easy to have\u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":486,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6814","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=6814"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6814\/revisions"}],"predecessor-version":[{"id":17911,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6814\/revisions\/17911"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/486"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=6814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}