Convex Analysis and Duality over Discrete Domains  

作　　者：Murat Adıvar Shu-Cherng Fang 

机构地区：[1]Department of Management,Marketing and Entrepreneurship,Fayetteville State University,Fayetteville,NC 28301,USA [2]Industrial and Systems Engineering,College of Engineering,North Carolina State University,Raleigh,NC 27695-7906,USA

出　　处：《Journal of the Operations Research Society of China》2018年第2期189-247,共59页中国运筹学会会刊（英文）

基　　金：This work has been supported by US Army Research Office Grant(No.W911NF-15-1-0223);The Scientific and Technological Research Council of Turkey Grant(No.1059B191300653).

摘　　要：The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.

关 键 词：Discrete convex analysis Discrete Lagrangian duality Discrete Slater’s condition Discrete strong duality Integer programming INTEGRALITY 

分 类 号：O17[理学—数学]