An auxiliary function method for constrained systems of nonlinear equations
- Authors: Wu, Zhiyou , Bai, Fusheng , Mammadov, Musa
- Date: 2008
- Type: Text , Conference paper
- Relation: Paper presented at 20th EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT-2008, Neringa, Lithuania : 20th-23rd May 2008 p. 259-265
- Full Text: false
- Description: In this paper, we propose an auxiliary function method to solve constrained systems of nonlinear equations. By introducing an auxiliary function, an unconstrained (box-constrained) optimization problem is constructed for a given constrained system of nonlinear equations. It is shown that any local minimizer of the constructed unconstrained optimization problem is an approximate solution to the given constrained system when parameters are appropriately chosen, and the precision for approximation can be preset. It is also shown that any accumulation point of the local minimizers of the constructed unconstrained optimization problems with a sequence of parameters tending to zero is a solution to the given constrained system of nonlinear equations.
A new auxiliary function method for general constrained global optimization
- Authors: Wu, Zhiyou , Bai, Fusheng , Yang, Yongjian , Mammadov, Musa
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Vol. 62, no. 2 (2013), p. 193-210
- Full Text:
- Reviewed:
- Description: In this article, we first propose a method to obtain an approximate feasible point for general constrained global optimization problems (with both inequality and equality constraints). Then we propose an auxiliary function method to obtain a global minimizer or an approximate global minimizer with a required precision for general global optimization problems by locally solving some unconstrained programming problems. Some numerical examples are reported to demonstrate the efficiency of the present optimization method. © 2013 Taylor & Francis.
- Description: 2003011103
A new auxiliary function method for systems of nonlinear equations
- Authors: Wu, Zhiyou , Bai, Fusheng , Li, Guoquan , Yang, Yongjian
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 11, no. 2 (2014), p. 345-364
- Full Text: false
- Reviewed:
- Description: In this paper, we present a new global optimization method to solve nonlinear systems of equations. We reformulate given system of nonlinear equations as a global optimization problem and then give a new auxiliary function method to solve the reformulated global optimization problem. The new auxiliary function proposed in this paper can be a filled function, a quasifilled function or a strict filled function with appropriately chosen parameters. Several numerical examples are presented to illustrate the effciency of the present approach.