Unified Duality Theory for Constrained Extremum Problems. Part I: Image Space Analysis

This paper is concerned with a unified duality theory for a constrained extremum problem. Following along with the image space analysis, a unified duality scheme for a constrained extremum problem is proposed by virtue of the class of regular weak separation functions in the image space. Some equivalent characterizations of the zero duality property are obtained under an appropriate assumption. Moreover, some necessary and sufficient conditions for the zero duality property are also established in terms of the perturbation function. In the accompanying paper, the Lagrange‐type duality, Wolfe duality and Mond–Weir duality will be discussed as special duality schemes in a unified interpretation. Simultaneously, three practical classes of regular weak separation functions will be also considered.