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A path following method for box-constrained multiobjective optimization with applications to goal programming problems

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  • Maria Cristina Recchioni

Abstract

We propose a path following method to find the Pareto optimal solutions of a box-constrained multiobjective optimization problem. Under the assumption that the objective functions are Lipschitz continuously differentiable we prove some necessary conditions for Pareto optimal points and we give a necessary condition for the existence of a feasible point that minimizes all given objective functions at once. We develop a method that looks for the Pareto optimal points as limit points of the trajectories solutions of suitable initial value problems for a system of ordinary differential equations. These trajectories belong to the feasible region and their computation is well suited for a parallel implementation. Moreover the method does not use any scalarization of the multiobjective optimization problem and does not require any ordering information for the components of the vector objective function. We show a numerical experience on some test problems and we apply the method to solve a goal programming problem. Copyright Springer-Verlag 2003

Suggested Citation

  • Maria Cristina Recchioni, 2003. "A path following method for box-constrained multiobjective optimization with applications to goal programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 69-85, September.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:1:p:69-85
    DOI: 10.1007/s001860300281
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    Citations

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    Cited by:

    1. Lourdes Uribe & Johan M Bogoya & Andrés Vargas & Adriana Lara & Günter Rudolph & Oliver Schütze, 2020. "A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems," Mathematics, MDPI, vol. 8(10), pages 1-29, October.
    2. Honggang Wang, 2013. "Zigzag Search for Continuous Multiobjective Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 654-665, November.
    3. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.

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