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1. A sufficient and necessary condition for global optimization

Author

Wu, Dong-Hua, Yu, Wu-Yang, and Zheng, Quan

Subjects
*MATHEMATICAL optimization, *MATHEMATICAL functions, *LEBESGUE integral, *ALGORITHMS, *DIFFERENTIAL equations, *MATHEMATICAL analysis
Abstract

Abstract: We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem. [Copyright &y& Elsevier]

Published
2010
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2. A new filled function method for unconstrained global optimization

Author

Wang, Chengjun, Yang, Yongjian, and Li, Jing

Subjects
*MATHEMATICAL functions, *MATHEMATICAL optimization, *INTEGER programming, *ALGORITHMS, *MATHEMATICAL analysis
Abstract

Abstract: In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Published
2009
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3. An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity

Author

Jian, Jin-Bao and Tang, Chun-Ming

Subjects
*ALGORITHMS, *MATHEMATICAL optimization, *STOCHASTIC convergence, *MATHEMATICAL functions, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]

Published
2005
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4. An improved vector particle swarm optimization for constrained optimization problems

Author

Sun, Chao-li, Zeng, Jian-chao, and Pan, Jeng-shyang

Subjects
*PARTICLE swarm optimization, *MATHEMATICAL optimization, *ALGORITHMS, *TRAJECTORIES (Mechanics), *EXPERIMENTS, *MATHEMATICAL analysis, *MATHEMATICAL functions, *MATHEMATICAL models
Abstract

Abstract: Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm , which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable. [ABSTRACT FROM AUTHOR]

Published
2011
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