Convex Maximization on a Convex Set With Fuzzy Constraints

Many people usually work for solving convex-minimization problems with various constraints, even including some fuzzy conditions. In this paper, we present some algorithms for solving convex-maximization problems with some fuzzy constraints. The objective function of the encountered problem is convex, but its feasible region is reverse convex. Even without fuzzy nature, the problem still remains in the category of NP-hardness, which can be solved in typical global optimization. We transform the reverse-convex feasible region to a difference of convex (d.c.) set, then solve the problem by combining the techniques of the d.c. method and the on-line vertices-enumeration method.