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
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- 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
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.
Gradient-free method for nonsmooth distributed optimization
- Authors: Li, Jueyou , Wu, Changzhi , Wu, Zhiyou , Long, Qiang
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol.61, no.2 (March 2014), p.325-340
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- Description: In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network. We first extend the (centralized) Nesterov’s random gradient-free algorithm and Gaussian smoothing technique to the distributed case. Then, the convergence of the algorithm is proved. Furthermore, an explicit convergence rate is given in terms of the network size and topology. Our proposed method is free of gradient, which may be preferred by practical engineers. Since only the cost function value is required, our method may suffer a factor up to d (the dimension of the agent) in convergence rate over that of the distributed subgradient-based methods in theory. However, our numerical simulations show that for some nonsmooth problems, our method can even achieve better performance than that of subgradient-based methods, which may be caused by the slow convergence in the presence of subgradient.
Sufficient conditions for global optimality of semidefinite optimization
- Authors: Quan, Jing , Wu, Zhiyou , Li, Guoquan , Wu, Ou
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Inequalities and Applications Vol. 2012, no. 108
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- Description: In this article, by using the Lagrangian function, we investigate the sufficient global optimality conditions for a class of semi-definite optimization problems, where the objective function are general nonlinear, the variables are mixed integers subject to linear matrix inequalities (LMIs) constraints as well as bounded constraints. In addition, the sufficient global optimality conditions for general nonlinear programming problems are derived, where the variables satisfy LMIs constraints and box constraints or bivalent constraints. Furthermore, we give the sufficient global optimality conditions for standard semi-definite programming problem, where the objective function is linear, the variables satisfy linear inequalities constraints and box constraints. © 2012 Quan et al.