Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems
- Authors: Wu, Zhiyou , Yang, Y. J. , Bai, Fusheng , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 151, no. 2 (2011), p. 241-259
- Full Text: false
- Reviewed:
- Description: The quadratic knapsack problem (QKP) maximizes a quadratic objective function subject to a binary and linear capacity constraint. Due to its simple structure and challenging difficulty, it has been studied intensively during the last two decades. This paper first presents some global optimality conditions for (QKP), which include necessary conditions and sufficient conditions. Then a local optimization method for (QKP) is developed using the necessary global optimality condition. Finally a global optimization method for (QKP) is proposed based on the sufficient global optimality condition, the local optimization method and an auxiliary function. Several numerical examples are given to illustrate the efficiency of the presented optimization methods. © 2011 Springer Science+Business Media, LLC.
A filled function method for nonlinear equations
- Authors: Wu, Zhiyou , Mammadov, Musa , Bai, Fusheng , Yang, Y. J.
- Date: 2007
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 189, no. 2 (2007), p. 1196-1204
- Full Text: false
- Reviewed:
- Description: In this paper, we propose a new global optimization approach based on the filled function method for solving box-constrained systems of nonlinear equations. The special properties of optimization problem are employed to construct a novel filled function. The objective function value can be reduced by half in each iteration of our filled function algorithm. Several numerical examples are presented to illustrate the efficiency of the present approach.
- Description: C1
- Description: 2003005618
A global optimization method for solving integer systems of equation
- Authors: Bai, Fusheng , Wu, Zhiyou , Yang, Y. J. , Mammadov, Musa
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 7th International Conference on Optimization: Techniques and Applications, ICOTA7, Kobe International Conference Center, Japan : 12th-15th December 2007
- Full Text: false
- Description: 2003005717
An auxiliary function method for systems of nonlinear equations
- Authors: Wu, Zhiyou , Bai, Fusheng , Mammadov, Musa , Yang, Y. J.
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 7th International Conference on Optimization: Techniques and Applications, ICOTA7, Kobe International Conference Center, Japan : 12th-15th December 2007
- Full Text: false
- Description: 2003005705