On Solving Optimization Problems with Hidden Nonconvex Structures

Alexander S. Strekalovsky ()
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Alexander S. Strekalovsky: Institute for System Dynamics and Control Theory of SB RAS

A chapter in Optimization in Science and Engineering, 2014, pp 465-502 from Springer

Abstract: 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.

Keywords: Bimatrix Game; Global Search Theory; Linear Complementarity Problem; Global Optimality Conditions (GOC); Special LSM (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0808-0_23

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DOI: 10.1007/978-1-4939-0808-0_23

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