CONVEX OPTIMIZATION ON MIXED DOMAINS

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.