Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem

Tibor Illes, Gábor Lovics

Research output: Book/ReportOther report

Abstract

In multi objective optimization problems several objective functions have to be minimized simultaneously. In this work, we present a new computational method for the numerical solution of the linearly constrained, convex multi objective optimization problem. We propose some technique to find joint decreasing direction for unconstrained and linearly constrained case as well. Based on these results we introduce a method using subdivision technique to approximate the whole Pareto-optimal set of the linearly constrained, convex multi objective optimization problem. Finally, we illustrate computations of our algorithm by solving the Markowitz-model on real data.
LanguageEnglish
Number of pages24
Volume2013
Publication statusPublished - 18 Apr 2013

Publication series

NameOperations Research Report
PublisherELTE
ISSN (Print)1215-5918

Fingerprint

Optimization problem
Multi-objective optimization
Approximation
Computational methods
Objective function
Numerical solution

Keywords

  • risk measurment
  • algorithm
  • vector optimization

Cite this

Illes, T., & Lovics, G. (2013). Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem. (Operations Research Report).
Illes, Tibor ; Lovics, Gábor. / Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem. 2013. 24 p. (Operations Research Report).
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Illes, T & Lovics, G 2013, Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem. Operations Research Report, vol. 2013.

Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem. / Illes, Tibor; Lovics, Gábor.

2013. 24 p. (Operations Research Report).

Research output: Book/ReportOther report

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AB - In multi objective optimization problems several objective functions have to be minimized simultaneously. In this work, we present a new computational method for the numerical solution of the linearly constrained, convex multi objective optimization problem. We propose some technique to find joint decreasing direction for unconstrained and linearly constrained case as well. Based on these results we introduce a method using subdivision technique to approximate the whole Pareto-optimal set of the linearly constrained, convex multi objective optimization problem. Finally, we illustrate computations of our algorithm by solving the Markowitz-model on real data.

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Illes T, Lovics G. Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem. 2013. 24 p. (Operations Research Report).