Weak duality theorem and complementary slackness theorem for linear matrix programming problems

Authors:
Ferenc Gyetvàn;Yong Shi
Affiliations:
Department of Mathematics, Institute of Quantitative Methods, School of Economics, Janus Pannonius University, Pécs, Hungary;College of Business Administration, University of Nebraska at Omaha, Omaha, NE 68182, USA
Venue:
Operations Research Letters
Year:
1992

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Abstract

In this paper we present a weak duality theorem and a complementary slackness theorem, which were omitted from the duality theory of the Gale-Kuhn-Tucker matrix optimization problem. We also show that the results are closely related to the duality of multiple-criteria and multiple-constraint level (MC^2) programming and the duality of multiobjective linear programming respectively.