A multidimensional descent method for global optimization
- Authors: Bagirov, Adil , Rubinov, Alex , Zhang, Jiapu
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 611-625
- Full Text: false
- Reviewed:
- Description: This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two-and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer.
Optimization approach for clustering datasets with weights
- Authors: Ghosh, Ranadhir , Rubinov, Alex , Zhang, Jiapu
- Date: 2005
- Type: Text , Journal article
- Relation: Optimization Methods & Software Vol. 20, no. 2-3 (Apr-Jun 2005), p. 329-345
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- Reviewed:
- Description: We introduce datasets with weights and suggest using the minimization of some highly nonsmooth functions for clustering of such datasets. Datasets with weights often appear as the result of an approximation of large-scale datasets. We examine such approximations and also consider the application of datasets with weights to examine self-organizing maps. Results of some numerical experiments are presented and discussed.
- Description: C1
- Description: 2003001366
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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- Reviewed:
- 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