Optimality Conditions in Vector Optimization

Indexed in: Scopus, EBSCO

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the ...
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Second Order Optimality Conditions in Vector Optimization Problems.

Pp. 35-60 (26)

DOI: 10.2174/978160805110611001010035

Author(s): M. Hachimi, B. Aghezzaf

Abstract

We are interested in proving optimality conditions for optimization problems. By means of different second-order tangent sets, various second-order necessary optimality conditions are obtained for both scalar and vector optimization problems where the feasible region is given as a set. We present also second-order sufficient optimality conditions so that there is only a very small gap with the necessary optimality conditions. As an application we establish second-order optimality conditions of Fritz John type, Kuhn-Tucker type 1, and Kuhn-Tucker type 2 for a problem with both inequality and equality constraints and a twice differentiable functions. At the end, a very general second-order necessary conditions for efficiency with respect to cones is present and it is applied to smooth and nonsmooth data.

Keywords:

Multiobjective programming, second-order tangent sets, constraint qualifications, second-order optimality conditions, efficient solutions.