Global optimality conditions and optimization methods for polynomial programming problems
- Authors: Wu, Zhiyou , Tian, Jing , Ugon, Julien
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 62, no. 4 (2015), p. 617-641
- Full Text: false
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- Description: This paper is concerned with the general polynomial programming problem with box constraints, including global optimality conditions and optimization methods. First, a necessary global optimality condition for a general polynomial programming problem with box constraints is given. Then we design a local optimization method by using the necessary global optimality condition to obtain some strongly or -strongly local minimizers which substantially improve some KKT points. Finally, a global optimization method, by combining the new local optimization method and an auxiliary function, is designed. Numerical examples show that our methods are efficient and stable.
Optimality conditions and optimization methods for quartic polynomial optimization
- Authors: Wu, Zhiyou , Tian, Jing , Quan, Jing , Ugon, Julien
- Date: 2014
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 232, no. (2014), p. 968-982
- Full Text: false
- Reviewed:
- Description: In this paper multivariate quartic polynomial optimization program (QPOP) is considered. Quartic optimization problems arise in various practical applications and are proved to be NP hard. We discuss necessary global optimality conditions for quartic problem (QPOP). And then we present a new (strongly or ε-strongly) local optimization method according to necessary global optimality conditions, which may escape and improve some KKT points. Finally we design a global optimization method for problem (QPOP) by combining the new (strongly or ε-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable.
Optimization methods for box-constrained nonlinear programming problems based on linear transformation and Lagrange interpolating polynomials
- Authors: Wu, Zhiyou , Bai, Fusheng , Tian, Jing
- Date: 2017
- Type: Text , Journal article
- Relation: Journal of the Operations Research Society of China Vol. 5, no. 2 (2017), p. 193-218
- Full Text: false
- Reviewed:
- Description: In this paper, an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials. Based on this condition, two new local optimization methods are developed. The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker (KKT) points in general. Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method. Some numerical examples are reported to show the effectiveness of the proposed methods. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.