On weak and strong Kuhn-Tucker conditions for smooth multiobjective optimization
The paper deals with smooth multiobjective optimization problems with inequality constraints. The following concepts are considered. Weak Kuhn-Tucker (WKT) optimality conditions are said to hold when not all the multipliers of the objective functions are zero, while strong Kuhn-Tucker (SKT) conditions are said to hold when all the multipliers of the objective functions are positive. The aim of the paper is to establish weak and strong Kuhn-Tucker necessary conditions for multiobjective optimization problems under the Guignard regularity condition (GRC) and the generalized Abadie regularity condition (GARC), respectively. The authors prove that GARC ensures SKT conditions for Geoffrion-properly efficient points. They show that GARC does not guarantee SKT for efficient points. For the special case, in which the feasible set is polyhedral and the objective functions are linear, they show that the assumption on Geoffrion-properly efficiency can be relaxed. It is shown that the condition GRC ensures WKT conditions for efficient points.
optimality conditions for efficient and Geoffrion-properly efficient solution
scientific article; zbMATH DE number 6136271