A General Approach to Dual Characterizations of Solvability of Inequality Systems with Applications

A general approach is developed to solvability theorems involving a broad class of functions, here called H-convex functions and inf-H-convex functions. The concept of Minkowski duality is exploited to provide dual characterizations for certain infinite inequality systems. The results not only cover the recently developed solvability results involving DSL functions, concave functions and difference of sublinear and convex functions but also include a new dual characterization for systems with completely difference convex functions. Detailed examples are provided to illustrate the broad nature of the results. Applications to global optimization are also given.