Mathematical Programming Computation最新文献

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">On <ns0:math><ns0:mi>O</ns0:mi> <ns0:mo>(</ns0:mo> <ns0:mi>n</ns0:mi> <ns0:mo>)</ns0:mo></ns0:math> algorithms for projection onto the top- <ns0:math><ns0:mi>k</ns0:mi></ns0:math> -sum sublevel set.","authors":"Jake Roth, Ying Cui","doi":"10.1007/s12532-024-00273-9","DOIUrl":"https://doi.org/10.1007/s12532-024-00273-9","url":null,"abstract":"<p><p>The <i>top-k-sum</i> operator computes the sum of the largest <math><mi>k</mi></math> components of a given vector. The Euclidean projection onto the top- <math><mi>k</mi></math> -sum sublevel set serves as a crucial subroutine in iterative methods to solve composite superquantile optimization problems. In this paper, we introduce a solver that implements two finite-termination algorithms to compute this projection. Both algorithms have <math><mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo></math> complexity of floating point operations when applied to a sorted <math><mi>n</mi></math> -dimensional input vector, where the absorbed constant <i>is independent of</i> <math><mi>k</mi></math> . This stands in contrast to an existing grid-search-inspired method that has <math><mi>O</mi> <mo>(</mo> <mi>k</mi> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo></math> complexity, a partition-based method with <math><mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>D</mi> <mspace></mspace> <mtext>log</mtext> <mspace></mspace> <mi>D</mi> <mo>)</mo></math> complexity, where <math><mi>D</mi> <mo>≤</mo> <mi>n</mi></math> is the number of distinct elements in the input vector, and a semismooth Newton method with a finite termination property but unspecified floating point complexity. The improvement of our methods over the first method is significant when <math><mi>k</mi></math> is linearly dependent on <math><mi>n</mi></math> , which is frequently encountered in practical superquantile optimization applications. In instances where the input vector is unsorted, an additional cost is incurred to (partially) sort the vector, whereas a full sort of the input vector seems unavoidable for the other two methods. To reduce this cost, we further derive a rigorous procedure that leverages approximate sorting to compute the projection, which is particularly useful when solving a sequence of similar projection problems. Numerical results show that our methods solve problems of scale <math><mi>n</mi> <mo>=</mo> <msup><mrow><mn>10</mn></mrow> <mrow><mn>7</mn></mrow> </msup> </math> and <math><mi>k</mi> <mo>=</mo> <msup><mrow><mn>10</mn></mrow> <mrow><mn>4</mn></mrow> </msup> </math> within 0.05 s, whereas the most competitive alternative, the semismooth Newton-based method, takes about 1 s. The existing grid-search method and Gurobi's QP solver can take from minutes to hours.</p>","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"17 2","pages":"307-348"},"PeriodicalIF":3.6,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12380050/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144973846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CP-Lib: Benchmark Instances of the Clique Partitioning Problem","authors":"Michael M. Sørensen, Adam N. Letchford","doi":"10.1007/s12532-023-00249-1","DOIUrl":"https://doi.org/10.1007/s12532-023-00249-1","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Self-adaptive ADMM for semi-strongly convex problems","authors":"Tianyun Tang, Kim-Chuan Toh","doi":"10.1007/s12532-023-00250-8","DOIUrl":"https://doi.org/10.1007/s12532-023-00250-8","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"42 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Domain-Driven Solver (DDS) Version 2.1: a MATLAB-based software package for convex optimization problems in domain-driven form","authors":"Mehdi Karimi, Levent Tunçel","doi":"10.1007/s12532-023-00248-2","DOIUrl":"https://doi.org/10.1007/s12532-023-00248-2","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"117 7-8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135511881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty","authors":"Bernard Knueven, David T. Mildebrath, Christopher Muir, John D. Siirola, J. Watson, D. L. Woodruff","doi":"10.1007/s12532-023-00247-3","DOIUrl":"https://doi.org/10.1007/s12532-023-00247-3","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"35 1","pages":"591 - 619"},"PeriodicalIF":6.3,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78372412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact methods for discrete Γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${varGamma }$$end{document}-robust interd","authors":"Yasmine Beck, Ivana Ljubić, Martin Schmidt","doi":"10.1007/s12532-023-00244-6","DOIUrl":"https://doi.org/10.1007/s12532-023-00244-6","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"232 1","pages":"733 - 782"},"PeriodicalIF":6.3,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89050628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing minimum-volume enclosing ellipsoids","authors":"Nathaniel Bowman, Michael T. Heath","doi":"10.1007/s12532-023-00242-8","DOIUrl":"https://doi.org/10.1007/s12532-023-00242-8","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"3 1","pages":"621 - 650"},"PeriodicalIF":6.3,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89241145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integer programming column generation: accelerating branch-and-price using a novel pricing scheme for finding high-quality solutions in set covering, packing, and partitioning problems","authors":"Stephen J. Maher, Elina Rönnberg","doi":"10.1007/s12532-023-00240-w","DOIUrl":"https://doi.org/10.1007/s12532-023-00240-w","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"14 1","pages":"1-40"},"PeriodicalIF":6.3,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80980553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Feasibility Jump: an LP-free Lagrangian MIP heuristic","authors":"Bjørnar Luteberget, Giorgio Sartor","doi":"10.1007/s12532-023-00234-8","DOIUrl":"https://doi.org/10.1007/s12532-023-00234-8","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"1 1","pages":"365-388"},"PeriodicalIF":6.3,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89976500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A branch and bound algorithm for robust binary optimization with budget uncertainty","authors":"Christina Büsing, Timo Gersing, A. Koster","doi":"10.1007/s12532-022-00232-2","DOIUrl":"https://doi.org/10.1007/s12532-022-00232-2","url":null,"abstract":"","PeriodicalId":47044,"journal":{"name":"Mathematical Programming Computation","volume":"12 1","pages":"269-326"},"PeriodicalIF":6.3,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77848007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}