A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints.

*(English)*Zbl 07250730Summary: This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems.

##### MSC:

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

90C26 | Nonconvex programming, global optimization |

##### Keywords:

neural network; mathematical programming with equilibrium constraints; asymptotically stability; globally convergence##### Software:

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\textit{S. Ezazipour} and \textit{A. Golbabai}, Kybernetika 56, No. 3, 383--409 (2020; Zbl 07250730)

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##### References:

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