Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems

This paper deals with robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of an uncertain semi-infinite multiobjective optimization problem. By using robust optimization and a modified $$\varepsilon $$ ε -constraint scalarization methodology, we first present the relationship between robust $$\varepsilon $$ ε -quasi solutions of the uncertain optimization problem and that of its corresponding scalar optimization problem. Then, we obtain necessary optimality conditions for robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of the uncertain optimization problem in terms of a new robust-type subdifferential constraint qualification. We also deduce sufficient optimality conditions for robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of the uncertain optimization problem under assumptions of generalized convexity. Besides, we introduce a Mixed-type robust $$\varepsilon $$ ε -multiobjective dual problem (including Wolfe type and Mond-Weir type dual problems as special cases) of the uncertain optimization problem, and explore robust $$\varepsilon $$ ε -quasi weak, $$\varepsilon $$ ε -quasi strong, and $$\varepsilon $$ ε -quasi converse duality properties. Furthermore, we introduce an $$\varepsilon $$ ε -quasi saddle point for the uncertain optimization problem and investigate the relationships between the $$\varepsilon $$ ε -quasi saddle point and the robust $$\varepsilon $$ ε -quasi Pareto efficient solution for the uncertain optimization problem.