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Optimization in Science and Engineering pp 465–502Cite as

On Solving Optimization Problems with Hidden Nonconvex Structures

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Abstract

Here we consider three very popular optimization problems: the linear complementarity problem, the search for Nash equilibria in a bimatrix game, and the quadratic-linear bilevel programming problem. It can be shown that each of the problem possesses a hidden nonconvexity and, as a consequence, a rather large number of local solutions which are different from global ones from the viewpoint of the goal function. In order to attack these problems the principal points of Global Search theory are presented and discussed. Furthermore, the main stages of Local and Global Search Methods are precised for each problem. Finally, we present the new results of computational solution separately for every problem considered.

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Author information

Authors and Affiliations

  1. Institute for System Dynamics and Control Theory of SB RAS, Lermontov St. 134, Irkutsk, 664033, Russia

    Alexander S. Strekalovsky

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  1. Alexander S. Strekalovsky
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Correspondence to Alexander S. Strekalovsky .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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Strekalovsky, A.S. (2014). On Solving Optimization Problems with Hidden Nonconvex Structures. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_23

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