Recent Advances in Mathematical Programming with Semi-continuous Variables and Cardinality Constraint

查看全文 作　　者：Xiaoling [1]Sun;Xiaojin [2]Zheng;Duan [3]Li

机构地区：[1]Department of Management Science,School of Management,Fudan University,Shanghai 200433,P.R.China;[2]School of Economics and Management,Tongji University,Shanghai 200092,P.R.China;[3]Department of Systems Engineering and Engineering Management,The Chinese University of Hong Kong,Shatin,N.T.,Hong Kong

出　　处：《Journal of the Operations Research Society of China》索引2013年第1卷第1期,共23页

基　　金：supported by the National Natural Science Foundation of China grants(Nos.11101092,10971034);the Joint National Natural Science Foundation of China/Research Grants Council of Hong Kong grant(No.71061160506);the Research Grants Council of Hong Kong grants(Nos.CUHK414808 and CUHK414610). 摘　　要：Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems. 关键词：Semi-continuous variables Cardinality and sparsity constraint Mixed-integer 0-1 quadratic programming Perspective reformulation Lagrangian decomposition Approximate methods

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Recent Advances in Mathematical Programming with Semi-continuous Variables and Cardinality Constraint

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