Optimization by level set methods. III: Characterizations of solutions in the presence of duality
Ivan Singer · Numerical Functional Analysis and Optimization · 1982
Let G be a non-empty subset of a real locally convex space F and h:F→[rbar] a functional. We give necessary and sufficient conditions in order that goεG should satisfy h(go)=inf h(G) and that there should hold one of the formulae of (weak or stronq) duality of [5], [6] for inf h(G). The conditions are similar to those of [5], [6], but involve some additional level sets of h.