Normal cones to a polyhedral convex set and generating efficient faces in linear multiobjective programming. (English) Zbl 0959.90042

Nguyen thi Bach Kim; Dinh The Luc

Acta Math. Vietnam. 25, No. 1, 101-124 (2000).

Summary: We describe the normal cones to a polyhedral convex set and their polarity with the faces of the set. Then we express optimality conditions in terms of negative normal cones and propose a method for generating efficient solution faces of a linear multiobjective programming problem together with some computational examples.

MSC:

90C29

Multi-objective and goal programming

Keywords:

normal cones; polyhedral convex set; optimality conditions; linear multiobjective programming problem