Introducing oblique norms into multiple criteria programming

Authors:
Bernd Schandl;Kathrin Klamroth;Margaret M. Wiecek
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC, USA/;Department of Computer Science and Mathematics, University of Applied Sciences Dresden, Dresden, Germany/;Department of Mathematical Sciences, Clemson University, Clemson, SC, USA (e-mail: wmalgor@clemson.edu)
Venue:
Journal of Global Optimization
Year:
2002

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Abstract

We propose to use block norms to generate nondominated solutions of multiple criteria programs and introduce the new concept of the oblique norm that is specially tailored to handle general problems. We prove the equivalence of finding the properly nondominated solutions of a multiple criteria program and solving its scalarization by means of oblique norms.