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Multiobjective Control Approximation Problems: Duality and Optimality

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  • G. Wanka

    (Technical University Chemnitz)

Abstract

A general convex multiobjective control approximation problem is considered with respect to duality. The single objectives contain linear functionals and powers of norms as parts, measuring the distance between linear mappings of the control variable and the state variables. Moreover, linear inequality constraints are included. A dual problem is established, and weak and strong duality properties as well as necessary and sufficient optimality conditions are derived. Point-objective location problems and linear vector optimization problems turn out to be special cases of the problem investigated. Therefore, well-known duality results for linear vector optimization are obtained as special cases.

Suggested Citation

  • G. Wanka, 2000. "Multiobjective Control Approximation Problems: Duality and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 457-475, May.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:2:d:10.1023_a:1004622204554
    DOI: 10.1023/A:1004622204554
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    References listed on IDEAS

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    Cited by:

    1. Khoirunnisa Rohadatul Aisy Muslihin & Endang Rusyaman & Diah Chaerani, 2022. "Conic Duality for Multi-Objective Robust Optimization Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    2. Haijun Liu & Neng Fan & Panos M. Pardalos, 2012. "Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 370-381, August.

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