Pseudo-lipschitzian continuity of solution mappings in parametrical optimi­zation problems
The study of the properties of solution mappings in parametrical optimization problems represents an urgent problem. Particularly, considerable efforts are directed to finding the conditions of different types of generalized Lipschitzian continuity of solution mappings, namely their calmness and pseudo-Lipschitzian continuity (also referred to as the Aubin property) [1]. A new interesting approach to investigating the calmness of solution mappings has recently been proposed by Canovas et al. [2] for parametrical linear programming problems and applied to a much wider range of problems by Klatte and Kummer [3]. In this approach, the calmness of solution mappings is related to the calmness of an associated system representing a constraint on the level set of the objective function on the domain of the problem. In our note, we propose to expand the use of the approach [3] for investigating the pseudo-Lipschitzian continuity of solution mappings. Several sufficient conditions for the pseudo-Lipschitzian continuity of solution mappings, as well as the generalization of the Hoffman lemma are presented.