{"id":1378,"date":"2023-02-15T19:23:58","date_gmt":"2023-02-15T19:23:58","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/6050\/"},"modified":"2023-02-15T19:23:58","modified_gmt":"2023-02-15T19:23:58","slug":"6050","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/6050\/","title":{"rendered":"6050"},"content":{"rendered":"<p>A quadratic programming model is an optimization model with <strong>n<\/strong> decision variables and <strong>m<\/strong> linear constraints, and of the form:<\/p>\n<p>Minimize Z=12xTQx+cTx &nbsp;\n<\/p>\n<p>Subject to: Ax\u2265b &nbsp;\n<\/p>\n<p>x\u22650 &nbsp;<\/p>\n<p>Where <strong>x<\/strong> is the n by 1 column vector of decision variables and <strong>x<\/strong>T is its transpose, <strong>Q<\/strong> is an n by n symmetric matrix of the objective parameters, <strong>c<\/strong> is an n by 1 vector of additional objective parameters, <strong>A<\/strong> is an m by n matrix of constraints parameters, and <strong>b<\/strong> is an m by 1 vector of constraints&#8217; right hand sides.<\/p>\n<ol>\n<li>Explain how quadratic programming is used in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting. Indicate explicitly and qualitatively what Z, <strong>x<\/strong>, <strong>Q<\/strong>, <strong>C<\/strong>, <strong>A<\/strong>, and b are in your example.<\/li>\n<li>Describe how you would handle solving a quadratic programming problem in which some of the problem parameters are random variables as opposed to being constant values. Make sure that you include a specific example of application in your response.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>A quadratic programming model is an optimization model with n decision variables and m linear constraints, and of the form: Minimize Z=12xTQx+cTx &nbsp; Subject to: Ax\u2265b &nbsp; x\u22650 &nbsp; Where x is the n by 1 column vector of decision variables and xT is its transpose, Q is an n by n symmetric matrix of [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[186],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/1378"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=1378"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/1378\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=1378"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=1378"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=1378"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=1378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}