Multiobjective semi-infinite optimization: Properly efficient solutions and local convexity
This lecture deals with multiobjective semi-infinite optimization problems which are defined by finitely many objective functions and infinitely many inequality constraints in a finite-dimensional space. We generalize two concepts of properly efficient solutions to the semi-infinite setting and present corresponding optimality conditions. We then discuss constraint qualifications as well as necessary and sufficient conditions for locally weakly efficient solutions. Furthermore, under a generic condition it is shown that locally around an efficient point the original problem can be transformed equivalently in such a way that the Lagrangian of the transformed weighted sum optimization problem becomes locally convex. Consequently, local duality theory and corresponding solution methods can be used after applying this convexification procedure. This is a joint work together with Francisco Guerra Vázquez from the Universidad de las Américas, Puebla, México.
Palabras clave / Keywords: multiobjective semi-infinite optimization proper efficiency constraint qualifications convexification
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