刊名：Journal of the Operations Research Society of China
题名：Convex Analysis and Duality over Discrete Domains
June 2018, Volume 6, Issue 2, pp189-247
作者： Murat Ad?var, Shu-Cherng Fang
单位：Fayetteville State University, North Carolina State University
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
全文链接https://link.springer.com/article/10.1007/s40305-017-0158-2