{"id":19211,"date":"2024-02-01T14:37:32","date_gmt":"2024-02-01T06:37:32","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=19211"},"modified":"2024-02-01T14:48:39","modified_gmt":"2024-02-01T06:48:39","slug":"talk20240227","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2024\/02\/01\/talk20240227\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u30102\u670827\u65e5\u3011Jan Harold Alcantara \/ Theoretical smoothing frameworks for nonsmooth bilevel optimization problems"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"19211\" class=\"elementor elementor-19211\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c5458f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c5458f6\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\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-43b8ceff\" data-id=\"43b8ceff\" 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-4115cdb6 elementor-widget elementor-widget-heading\" data-id=\"4115cdb6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Theoretical smoothing frameworks for nonsmooth bilevel optimization problems<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-699139af elementor-widget elementor-widget-spacer\" data-id=\"699139af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-619e1f6 elementor-widget elementor-widget-text-editor\" data-id=\"619e1f6\" 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><strong><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal;\">Time:<\/span><\/strong><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\"> February 27 (Tuesday) 14:00-15:00<br \/><\/span><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">Place: S506, Gongguan Campus, NTNU<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11dc7f58 elementor-widget elementor-widget-image\" data-id=\"11dc7f58\" 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=\"465\" height=\"464\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2024\/02\/20240227_JanHaroldAlcantara_.png\" class=\"attachment-full size-full wp-image-19214\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2024\/02\/20240227_JanHaroldAlcantara_.png 465w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2024\/02\/20240227_JanHaroldAlcantara_-300x300.png 300w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2024\/02\/20240227_JanHaroldAlcantara_-150x150.png 150w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/>\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<div class=\"elementor-element elementor-element-33877fad elementor-widget elementor-widget-text-editor\" data-id=\"33877fad\" 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<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\">Dr. Jan Harold Alcantara<\/div><div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 18px; line-height: 22px; text-align: center; color: #cc9966; font-weight: bold;\">( Research fellow of RIKEN)<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5de4ac7d elementor-widget elementor-widget-spacer\" data-id=\"5de4ac7d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cf4b31e elementor-widget elementor-widget-text-editor\" data-id=\"cf4b31e\" 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;\">The optimal value function approach provides a useful reformulation of the bilevel optimization problem, but its utility is often hindered by the nonsmoothness of the value function even in cases when the associated lower-level function is smooth. In this talk, we present two smoothing strategies for the value function associated with lower-level functions that are not necessarily smooth but are Lipschitz continuous. The first method employs a quadratic regularization approach for partially convex lower-level functions, while the second utilizes entropic regularization for general lower-level objective functions. Meanwhile, the property known as gradient consistency is crucial in ensuring that a designed smoothing algorithm is globally subsequentially convergent to stationary points of the equivalent reformulation of the bilevel problem. With this in mind, we show that the proposed smooth approximations satisfy the gradient consistent property under certain conditions on the lower-level function.<\/span><\/p><h3><span style=\"color: #000000;\">Organizer: Jein-Shan Chen<\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d369826 elementor-widget elementor-widget-image\" data-id=\"d369826\" 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 decoding=\"async\" width=\"1240\" height=\"758\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full wp-image-7367\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Theoretical smoothing frameworks for nonsmooth bilevel  [&hellip;]<\/p>\n","protected":false},"author":23,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"off","ocean_gallery_id":[],"footnotes":""},"categories":[1,124],"tags":[],"class_list":["post-19211","post","type-post","status-publish","format-standard","hentry","category-news","category-speeches","entry"],"_links":{"self":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/19211","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=19211"}],"version-history":[{"count":10,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/19211\/revisions"}],"predecessor-version":[{"id":19223,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/19211\/revisions\/19223"}],"wp:attachment":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=19211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=19211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=19211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}