Constrained optimization using multiple objective programming |
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Authors: | Kathrin Klamroth Tind Jørgen |
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Institution: | 1.Institute of Applied Mathematics,University of Erlangen-Nuremberg,Erlangen,Germany;2.Department of Applied Mathematics and Statistics, Institute for Mathematical Sciences,University of Copenhagen,Copenhagen ?,Denmark |
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Abstract: | In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently
suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently
realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches
are specifically designed to incorporate such complex preference structures, they gain more and more importance in application
areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems
both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share
important properties, and that many classical solution approaches have correspondences in the respective models. The analysis
naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming
problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence
results are proven for convex and nonconvex problems. |
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Keywords: | Constrained optimization Multiple objective programming Lagrange multipliers Convergence |
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