Optimization by level set methods. IV: Generalizations and complements
Ivan Singer · Numerical Functional Analysis and Optimization · 1982
We consider the optimization problem inf h(G),_where G≠Ø is a subset of a real locally convex space F and h:F→[Rbar].§1 contains a unified approach to the necessary and sufficient conditions of [l3]–[l5] and of §§2–3. In §§2–3 we give conditions for the validity of duality formulae involving half-spaces (closed or open), unions of strips and unions of closed strips, containing G. In §4 we show some relations between the minimization of h and hq (the quasi-convex hull of h) on G and ∞ G, or ∞[bbar] G and we determine . In §5 we consider duality formulae involving nonlinear functionals.