杂志名：Journal of Industrial and Management Optimization (JIMO)

论文题目：Convex optimization on mixed domains

连接：http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6865
Pages: 189 - 227, Volume 8, Issue 1, February 2012
doi:10.3934/jimo.2012.8.189       Abstract       References       Full Text (849.2K)       Purchase Paper (30.00 USD)
Murat Adivar - Izmir University of Economics, Department of Mathematics, 35330, Balcova, Izmir, Turkey (email)
Shu-Cherng Fang - Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695-7906, United States (email)

Abstract: This paper aims to study convex analysis on some “generalized domains,” in particular, the domain of the product of closed subsets of reals. We introduce the basic concepts and derive analytic properties regarding convex subsets of mixed domains and convex functions defined on convex sets in mixed domains. The results obtained may open an avenue for modeling and solving a new type of optimization problems that involve both discrete and continuous variables at the same time.
Keywords:  Continuous optimization, convexity, convex optimization, discrete optimization, generalized convexity, subgradient, time scales.
Mathematics Subject Classification:  Primary 90C25, 80M50; Secondary 65K05, 90C30.
Received: April 2011;      Revised: August 2011;      Published: November 2011.