OPTIMALITY RESULTS FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH VANISHING CONSTRAINTS
Tadeusz Antczak · Journal of Applied Analysis & Computation · 2023
At present, some real extremum problems related to the activity of modern man, for example, in industry, economy, optimal control, engineering, mechanics, are modeled by optimization problems with vanishing constraints. In this paper, a class of nondifferentiable vector optimization problems with vanishing constraints is considered in which every component of the involved functions is locally Lipschitz. This kind of extremum problems is generally difficult to deal with, because of a special structure of constraints. The Karush-Kuhn-Tucker necessary optimality conditions are established for foregoing nonsmooth multicriteria optimization problems under the VC-Cottle constraint qualification. Sufficient optimality conditions are also proved for the considered nondifferentiable vector optimization problem with vanishing constraints under convexity hypotheses.