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.
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
An integral function and vector sequence method for unconstrained global optimization
- Authors: Yang, Yongjian , Bai, Fusheng
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 50, no. 2 (2011), p. 293-311
- Full Text: false
- Reviewed:
- Description: An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm. © Springer Science+Business Media, LLC. 2010.
A filled function method for constrained nonlinear equations
- Authors: Bai, Fusheng , Mammadov, Musa , Wu, Zhiyou , Yang, Yongjian
- Date: 2008
- Type: Text , Journal article
- Relation: Pacific Journal of Optimization Vol. 4, no. 1 (Jan 2008), p. 9-18
- Full Text: false
- Reviewed:
- Description: We consider the problem of solving a constrained system of nonlinear equations. After reformulating the system into an equivalent constrained global optimization problems, we construct a filled function based on a special property of the reformulated problem. A filled function method is then proposed to solve the constrained system of nonlinear equations. Some numerical examples are presented to illustrate the usefulness of the present techniques.
- Description: C1
Lower order calmness and exact penalty function
- Authors: Bai, Fusheng , Wu, Zhiyou , Zhu, D.
- Date: 2006
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 21, no. 4 (2006), p. 515-526
- Full Text: false
- Reviewed:
- Description: In this article, we investigate the exact penalty properties of a lower order penalty function under a lower order calmness conditions. It is shown that the local exact penalization of the lower order penalty function with any positive penalty parameter holds under the local lower order calmness condition. A necessary and sufficient condition for global exact penalization of the lower order penalty function is given in terms of global lower order calmness condition. Furthermore, a formula of least global exact penalty parameter for the lower order penalty function is obtained.
- Description: C1
- Description: 2003002855