ABSTRACT
The dual characterizations of the solution set of an optimization problem having multiple optimal solutions are of fundamental importance. It is useful in characterizing the boundedness of the solution sets as well as in understanding the behavior of solution methods. It is well known that the Lagrange multiplier is a key to identify the optimal solutions of a constrained optimization problem. In 1988, Mangasarian [177] presented simple and elegant characterizations of the solution set for a convex minimization problem over a convex set, when one solution is known. Jeyakumar et al. [115] have established that the Lagrangian function of an inequality constrained convex optimization problem is constant on the solution set. They employed this property of Lagrangian to establish several Lagrange multiplier characterizations of the solution set of a convex optimization problem. Dinh et al. [67] presented several Lagrange multiplier characterizations of a pseudolinear optimization problem over a closed convex set with linear inequality constraints. Recently, Lalitha and Mehta [156] derived some Lagrange multiplier characterizations of the solution set of an optimization problem involving pseudolinear functions in terms of bifunction h. Very recently, Mishra et al. [200] established Lagrange multiplier characterizations for the solution sets of nonsmooth constrained optimization problems by using the properties of locally Lipschitz pseudolinear functions.
