Generalized robust duality in constrained nonconvex optimization

Abstract

ABSTRACT In this paper, the general dual problems in robust optimization without any convexity or concavity assumptions are investigated by using the image space analysis. A generalized Lagrange function is proposed by the class of regular weak separation functions. Then, two types of generalized robust dual problems are established. Under the appropriate assumption, the equivalent assertions of the zero duality gap property are characterized between the robust counterpart of an uncertain constrained optimization problem and the optimistic counterpart of its uncertain generalized Lagrange dual. Similarly, these theories and results can be extended to the deterministic dual pair of the robust counterpart and its Lagrange dual.