{"topic":{"id":4546,"title":"奇妙的 max-min ineqality","slug":"topic","userId":1047,"categoryId":54,"createdAt":"2023-07-28 08:38:42.753134","bumpedAt":"2024-01-01 03:27:08.295989","views":259,"postsCount":2,"highestPostNumber":2,"likeCount":0,"closed":false,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"The max-min inequality For any function f:X×Y→R: f: \\mathcal{X} \\times \\mathcal{Y} \\rightarrow \\mathbb{R}: f:X×Y→R: maxx∈Xminy∈Yf(x,y)≤miny∈Ymaxx∈Xf(x,y) max_{x \\in \\mathcal{X} } {min_{y \\in \\mathcal{Y} } {f(x, y)}} \\le…","deletedAt":null,"isAnonymous":false,"isPrivate":false,"isMembersOnly":false,"category":{"id":54,"name":"学术专区","slug":"academic","color":"9EB83B"},"author":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif"},"realAuthor":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif"},"tags":["math","optimization"]},"posts":[{"id":8116,"postNumber":1,"raw":"**The max-min inequality**\nFor any function\n$$ \n f: \\mathcal{X} \\times \\mathcal{Y} \\rightarrow \\mathbb{R}: \n$$ \n\n$$ \nmax_{x \\in \\mathcal{X} } {min_{y \\in \\mathcal{Y} } {f(x, y)}} \\le \nmin_{y \\in \\mathcal{Y} } {max_{x \\in \\mathcal{X} } {f(x, y)}}\n$$\n\n![_Convex Optimization Basics oLowhs83aHk-03|690x388](/uploads/image/f3/a6/f3a6931adc5fde25b0e97e5a63f52e1f4b6d0d9eba619c86c8f494977a392160.avif)\n\n好的里面挑差的总是比差的里面挑好的要好。","cooked":"

The max-min inequality
\nFor any function
\n

\nf: \\mathcal{X} \\times \\mathcal{Y} \\rightarrow \\mathbb{R}:\n

\nmax_{x \\in \\mathcal{X} } {min_{y \\in \\mathcal{Y} } {f(x, y)}} \\le \nmin_{y \\in \\mathcal{Y} } {max_{x \\in \\mathcal{X} } {f(x, y)}}\n

$\"_Convex$

好的里面挑差的总是比差的里面挑好的要好。

\n","createdAt":"2023-07-28 08:38:42.941647","updatedAt":"2024-03-17 13:05:01.646508","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":61,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"👍️","count":1,"users":[{"id":178,"username":"Hypocrisy","name":"rotartsinimdA"}],"hasReacted":false}],"wiki":false,"version":6,"publicVersion":6,"deletedAt":null,"isAnonymous":false,"user":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8152,"postNumber":2,"raw":"满足弱对偶性。","cooked":"

满足弱对偶性。

\n","createdAt":"2023-07-28 09:22:14.613852","updatedAt":"2023-07-28 09:22:14.613852","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":7,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":991,"username":"Siyuan","name":"Siyuan Wu","avatarUrl":"/uploads/image/7e/87/7e87136b5ed7cec7b65929e40d5f4a7be35578a674bc7f3cfafffcdad2783215.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}}],"hasMore":false,"lastReadPostNumber":2,"hasUrlPostNumber":true}