{"id":28203,"date":"2026-05-21T11:19:08","date_gmt":"2026-05-21T03:19:08","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=28203"},"modified":"2026-05-21T11:22:59","modified_gmt":"2026-05-21T03:22:59","slug":"lecture20260615","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2026\/05\/21\/lecture20260615\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u30106\u670815\u65e5\u3011Sven Leyffer\uff0fSolving Massive Combinatorial Optimization Problems"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"28203\" class=\"elementor elementor-28203\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-655e11e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"655e11e\" 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-a7bdcce\" data-id=\"a7bdcce\" 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-d1f5c12 elementor-widget elementor-widget-image\" data-id=\"d1f5c12\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/05\/20260615\u6d77\u5831_Sven_Leffer\u6559\u6388s-724x1024.png\" class=\"attachment-large size-large wp-image-28205\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/05\/20260615\u6d77\u5831_Sven_Leffer\u6559\u6388s-724x1024.png 724w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/05\/20260615\u6d77\u5831_Sven_Leffer\u6559\u6388s-212x300.png 212w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/05\/20260615\u6d77\u5831_Sven_Leffer\u6559\u6388s-768x1086.png 768w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/05\/20260615\u6d77\u5831_Sven_Leffer\u6559\u6388s.png 992w\" sizes=\"(max-width: 724px) 100vw, 724px\" \/>\t\t\t\t\t\t\t\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-c707c36 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c707c36\" 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-bb10535\" data-id=\"bb10535\" 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-1a2f19b elementor-widget elementor-widget-text-editor\" data-id=\"1a2f19b\" 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<p><span style=\"color: #000000;\"><strong>Abstract<\/strong><\/span><br \/><span style=\"color: #000000;\">Many design, planning and decision problems arising in engineering, sciences, finance, and statistics can be modeled as mixed-integer nonlinear optimization problems. A challenging class of mixedinteger problems are topology design problem, arising in additive manufacturing or the design of cloaking devices. In topology optimization, the physical response of the design is modeled as partial-differential equations (PDEs) and the design is modeled with binary variables defined on each element of the discretization of the PDE. This approach results in mixed integer PDE-constrained optimization (MIPDECO) problem that combine the computational challenges of PDEs with the combinatorial challenges of a massive number of discrete variables. We a number of efficient and scalable optimization algorithms based on rounding and randomized search techniques and discuss their optimality properties. We illustrate these solution techniques with examples from topology optimization.<\/span><\/p>\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>\n\t\t","protected":false},"excerpt":{"rendered":"<p>AbstractMany design, planning and decision problems ari 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