A new local and global optimization method for mixed integer quadratic programming problems
- Authors: Li, G. Q. , Wu, Zhiyou , Quan, Jing
- Date: 2010
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 217, no. 6 (2010), p. 2501-2512
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- Description: In this paper, a new local optimization method for mixed integer quadratic programming problems with box constraints is presented by using its necessary global optimality conditions. Then a new global optimization method by combining its sufficient global optimality conditions and an auxiliary function is proposed. Some numerical examples are also presented to show that the proposed optimization methods for mixed integer quadratic programming problems with box constraints are very efficient and stable. Crown Copyright © 2010.
Global optimality conditions and optimization methods for quadratic integer programming problems
- Authors: Wu, Zhiyou , Li, Gloria , Quan, Jing
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 51, no. 3 (2011), p. 549-568
- Full Text: false
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- Description: In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable. © 2011 Springer Science+Business Media, LLC.
Global optimality conditions for mixed integer weakly concave programming problems
- Authors: Wu, Zhiyou , Quan, Jing , Bai, Fusheng
- Date: 2010
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 675-685
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- Description: In this paper, some necessary and some suffcient global optimality conditions for a class of mixed integer programming problems whose objective functions are the difference of quadratic functions and convex functions are established. The numerical examples are also presented to show the significance of the global optimality conditions for this class of programming problems. Copyright © 2010 Watam Press.
Global optimality conditions for some classes of polynomial integer programming problems
- Authors: Quan, Jing , Wu, Zhiyou , Li, Guoquan
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 7, no. 1 (2011), p. 67-78
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- Description: In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity.
Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables
- Authors: Wu, Zhiyou , Quan, Jing , Li, G. Q. , Tian, Jing
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. , no. (2011), p. 1-28
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- Description: Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient. © 2011 Springer Science+Business Media, LLC.
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
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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.
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.