Study on convergence of optimization problems

Abstract

In this thesis, various notions of convergence of sequence of sets and functions and their applications in the convergence of the optimal values under the perturbations of the constrained set and/or the objective function are presented. Also, we present the conditions under which a sequence of constrained convex, non-convex optimization problems converge in some sense to the given constrained convex, non-convex optimization problem. Further, Hadamard Well-Posedness with respect to SP convergence is defined and compared with Strong Well-Posedness, newlineLevitin-Polyak Well-Posedness and Tykhonov Well-Posedness. Also some newlineWell-Posedness theories are developed for B-vex optimization problems. newline newline