{"id":466,"date":"2017-11-06T10:42:55","date_gmt":"2017-11-06T10:42:55","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=466"},"modified":"2024-12-19T04:14:43","modified_gmt":"2024-12-19T04:14:43","slug":"optimization-2","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/optimization-2\/","title":{"rendered":"Optimization"},"content":{"rendered":"<section class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_column_text]<strong>Course: <\/strong>\u00a0MAT 453 3.0 Optimization (Compulsory)<\/p>\n<p style=\"text-align: justify;\"><strong>Course content:\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\">Maximizing\/ minimizing objective function, Constraints, Categories of optimization problems and several illustrations; Functions of one variable\/ several variables, Critical points, Maximizers and minimizers, Optimization with Hessian matrix of a function (quadratic forms, definiteness, principal minors), Optimization with Coercive functions; Convex sets, Convex functions, Optimization results associated with convexity, Convexity and Arithmetic-Geometric Mean Inequality; Newton\u2019s Method, The\u00a0\u00a0 Method of Steepest Decent,\u00a0 Beyond Steepest Decent; Least Square Fit,\u00a0 Subspaces and Projections,\u00a0 Minimum Norm Solutions of Underdetermined Linear Systems; : Convex programming; Karush-Kuhn-Tucker Theorem and Constrained Geometric Programming, Dual Convex Programming; History of Optimization- Classical Problems, Euler- Lagrange equation, Solutions of Classical Problems using Euler- Lagrange Equation.<\/p>\n<p><strong>\u00a0<\/strong><strong>Recommended Readings: <\/strong><\/p>\n<ol>\n<li>Peressini, A. L., Sullivan, F. E., &amp; Uhl, J. J., Jr. (1988). <em>The Mathematics of Nonlinear Programming (Undergraduate Texts in Mathematics)<\/em>. Springer.<\/li>\n<li>Hoffmann, L.D, Bradley, G.L., &amp; Rosen, K.H. (2005). <em>Applied Calculus: For Business, Economics, and the Social and Life Sciences, 8th Expanded Edition<\/em> (8th ed.). McGraw Hill.<\/li>\n<li>Applied Calculus \u2013 L.D. Hoffmann, G.L. Bradley, K.H. Rosen<\/li>\n<li>Blischke, W. R., &amp; Murthy, P. D. N. (2000). <em>Reliability: Modeling, Prediction, and Optimization<\/em> (1st ed.). Wiley.<\/li>\n<li>Bittinger, M. L., Ellenbogen, D. J., &amp; Surgent, S. J. (2012). <em>Calculus and Its Applications (10th Edition)<\/em> (10th ed.). Pearson.<\/li>\n<\/ol>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/section>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text]Course: \u00a0MAT 453 3.0 Optimization (Compulsory) Course content:\u00a0 Maximizing\/ minimizing objective function, Constraints, Categories of optimization problems and several illustrations; Functions of one variable\/ several variables, Critical points, Maximizers and minimizers, Optimization with Hessian matrix of a function (quadratic forms, definiteness, principal minors), Optimization with Coercive functions; Convex sets, Convex functions, Optimization results associated with &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/optimization-2\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Optimization<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/466"}],"collection":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/comments?post=466"}],"version-history":[{"count":5,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/466\/revisions"}],"predecessor-version":[{"id":4710,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/466\/revisions\/4710"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}