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Multiple Optimal Solutions In Quadratic Programming Models

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  • Paris, Quirino

Abstract

The problem of determining whether quadratic programming models possess either unique or multiple optimal solutions is important for empirical analyses which use a mathematical programming framework. Policy recommendations which disregard multiple optimal solutions (where they exist) are potentially incorrect and less than efficient. This paper proposes a strategy and the associated algorithm for finding all optimal solutions to any positive semidefinite linear complementarity problem. One of the main results is that the set of complementary solutions is convex. Although not obvious, this proposition is analogous to the well-known result in linear programming which states that any convex combination of optimal solutions is itself optimal.

Suggested Citation

  • Paris, Quirino, 1983. "Multiple Optimal Solutions In Quadratic Programming Models," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 8(2), pages 1-14, December.
    • Handle: RePEc:ags:wjagec:32089
    DOI: 10.22004/ag.econ.32089
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    File URL: https://ageconsearch.umn.edu/record/32089/files/08020141.pdf
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    References listed on IDEAS

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    1. Quirino Paris, 1981. "Multiple Optimal Solutions in Linear Programming Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 63(4), pages 724-727.
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    Cited by:

    1. Quirino Paris & Sophie S. Drogue & Giovanni Anania, 2009. "Calibrating mathematical programming spatial models [Calibrage pour les modèles spatiaux de programmation mathématique]," Post-Print hal-02754337, HAL.
    2. Paris, Quirino & Drogué, Sophie & Anania, Giovanni, 2011. "Calibrating spatial models of trade," Economic Modelling, Elsevier, vol. 28(6), pages 2509-2516.
    3. Yu-Ching Lee & Jong-Shi Pang & John Mitchell, 2015. "An algorithm for global solution to bi-parametric linear complementarity constrained linear programs," Journal of Global Optimization, Springer, vol. 62(2), pages 263-297, June.

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