Solvability Theorems Involving Inf-Convex Functions

This paper presents a unified theory on solvability of certain general systems of inequalities involving functions expressible as the pointwise infimum of convex functions. The approach used to develop these solvability theorems relies on Minkowski duality. Extensions of Farkas′ lemma and other solvability theorems are developed, both with and without a regularity condition, with applications to optimization.