On recent existence theorems in the theory of optimization

Abstract

A condition recently proposed is shown to imply the weak compactness in H 1,1 and actually is equivalent to another condition previously proposed by the authors. Once compactness is proved, then existence theorems follow from lower closure theorems also previously proved by the authors, and extended to Pareto problems. The present analysis adds to the recent work of Goodman concerning the equivalence of seminormality conditions with concepts of convex analysis and lattice theory.