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
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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.
Global optimality conditions and optimization methods for constrained polynomial programming problems
- Authors: Wu, Zhiyou , Tian, Jing , Ugon, Julien , Zhang, Liang
- Date: 2015
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 262, no. (2015), p. 312-325
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- Description: The general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality conditions for problem (GPP) are established. Then, a new local optimization method for this problem is proposed by exploiting these necessary global optimality conditions. A global optimization method is proposed for this problem by combining this local optimization method together with an auxiliary function. Some numerical examples are also given to illustrate that these approaches are very efficient. (C) 2015 Elsevier Inc. All rights reserved.
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
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- 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.