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

Soraya Ezazipour; Ahmad Golbabai

Kybernetika (2020)

  • Volume: 56, Issue: 3, page 383-409
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Ezazipour, Soraya, and Golbabai, Ahmad. "A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints." Kybernetika 56.3 (2020): 383-409. <http://eudml.org/doc/297375>.

@article{Ezazipour2020,
abstract = {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.},
author = {Ezazipour, Soraya, Golbabai, Ahmad},
journal = {Kybernetika},
keywords = {neural network; mathematical programming with equilibrium constraints; asymptotically stability; globally convergence},
language = {eng},
number = {3},
pages = {383-409},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints},
url = {http://eudml.org/doc/297375},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Ezazipour, Soraya
AU - Golbabai, Ahmad
TI - A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 3
SP - 383
EP - 409
AB - 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.
LA - eng
KW - neural network; mathematical programming with equilibrium constraints; asymptotically stability; globally convergence
UR - http://eudml.org/doc/297375
ER -

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