Global optimality conditions for some classes of optimization problems
- Authors: Wu, Zhiyou , Rubinov, Alex
- Date: 2009
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 145, no. 1 (2009), p. 164-185
- Full Text: false
- Reviewed:
- Description: We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract convexity. © 2009 Springer Science+Business Media, LLC.
Methods for global optimization of nonsmooth functions with applications
- Authors: Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Applied and Computational Mathematics Vol. 5, no. 1 (2006), p. 3-15
- Full Text: false
- Reviewed:
- Description: In this survey paper we present some results obtained in the Centre for Informatics and Applied Optimization (CIAO) at University of Ballarat, Australia, in the area of numerical global optimization. We describe a conceptual scheme of two methods developed in CIAO and present results of numerical experiments with some real world problems. The paper is based on a plenary lecture given by the author at the First International Conference on Control and Optimization with Industrial Applications, Baku, Azerbaijan, 2005.
- Description: C1
- Description: 2003001547
Local optimization method with global multidimensional search
- Authors: Bagirov, Adil , Rubinov, Alex , Zhang, Jiapu
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 32, no. 2 (2005), p. 161-179
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- Description: This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithms allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima. © Springer 2005.
- Description: C1
- Description: 2003001351
A global optimization approach to classification
- Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John
- Date: 2002
- Type: Text , Journal article
- Relation: Optimization and Engineering Vol. 9, no. 7 (2002), p. 129-155
- Full Text: false
- Reviewed:
- Description: In this paper is presented an hybrid algorithm for finding the absolute extreme point of a multimodal scalar function of many variables. The algorithm is suitable when the objective function is expensive to compute, the computation can be affected by noise and/or partial derivatives cannot be calculated. The method used is a genetic modification of a previous algorithm based on the Prices method. All information about behavior of objective function collected on previous iterates are used to chose new evaluation points. The genetic part of the algorithm is very effective to escape from local attractors of the algorithm and assures convergence in probability to the global optimum. The proposed algorithm has been tested on a large set of multimodal test problems outperforming both the modified Prices algorithm and classical genetic approach.
- Description: C1
- Description: 2003000061