A dynamical model for solving degenerate quadratic minimax problems with constraints.

*(English)*Zbl 1229.90262Summary: This paper presents a new neural network model for solving degenerate quadratic minimax (DQM) problems. On the basis of the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the DQM problems. It is also shown that the proposed network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.

##### MSC:

90C47 | Minimax problems in mathematical programming |

90C20 | Quadratic programming |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

37B25 | Stability of topological dynamical systems |

##### Keywords:

neural network; dynamic system; minimax problem; quadratic programming problem; convergent; stability
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\textit{A. R. Nazemi}, J. Comput. Appl. Math. 236, No. 6, 1282--1295 (2011; Zbl 1229.90262)

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