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.
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
- Full Text:
- 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
An algorithm for clustering based on non-smooth optimization techniques
- Authors: Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: International Transactions in Operational Research Vol. 10, no. 6 (2003), p. 611-617
- Full Text: false
- Reviewed:
- Description: The problem of cluster analysis is formulated as a problem of non-smooth, non-convex optimization, and an algorithm for solving the cluster analysis problem based on non-smooth optimization techniques is developed. We discuss applications of this algorithm in large databases. Results of numerical experiments are presented to demonstrate the effectiveness of this algorithm.
- Description: C1
- Description: 2003000422
Cutting angle method and a local search
- Authors: Bagirov, Adil , Rubinov, Alex
- Date: 2003
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 27, no. 2-3 (Nov 2003), p. 193-213
- Full Text: false
- Reviewed:
- Description: The paper deals with combinations of the cutting angle method in global optimization and a local search. We propose to use special transformed objective functions for each intermediate use of the cutting angle method. We report results of numerical experiments which demonstrate that the proposed approach is very beneficial in the search for a global minimum.
- Description: C1
- Description: 2003000438
Lagrange-type functions in constrained optimization
- Authors: Rubinov, Alex , Yang, Xiao , Bagirov, Adil , Gasimov, Rafail
- Date: 2003
- Type: Text , Journal article
- Relation: Journal of Mathematical Sciences Vol. 115, no. 4 (2003), p. 2437-2505
- Full Text: false
- Reviewed:
- Description: We examine various kinds of nonlinear Lagrange-type functions for constrained optimization problems. In particular, we study the weak duality, the zero duality gap property, and the existence of an exact parameter for these functions. The paper contains a detailed survey of results in these directions and comparison of different methods proposed by different authors. Some new results are also given.
- Description: C1
- Description: 2003000358
Optimization based clustering algorithms in multicast group hierarchies
- Authors: Jia, Long , Ouveysi, Iradj , Rubinov, Alex , Bagirov, Adil
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the 2003 Australian Telecommunications Networks and Applications Conference, Melbourne : 8th - 10th December, 2003
- Full Text:
- Reviewed:
- Description: In this paper we propose the use of optimization based clustering algorithms to determine hierarchical multicast trees. This problem is formulated as an optimization problem with a non-smooth, non-convex objective function. Different algorithms are examined for solving this problem. Results of numerical experiments using some artificial and real-world databases are reported. We compare several optimization based clustering methods and their combinations with the k- means method. The results demonstrate the effectiveness of these algorithms.
- Description: E1
- Description: 2003000382
Penalty functions with a small penalty parameter : Numerical experiments
- Authors: Bagirov, Adil , Rubinov, Alex
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at Industrial Optimization Conference 2003, Perth : 30th September, 2002
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000432
Unsupervised and supervised data classification via nonsmooth and global optimisation
- Authors: Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: Top Vol. 11, no. 1 (2003), p. 1-92
- Full Text:
- Reviewed:
- Description: We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss results of numerical experiments.
- Description: C1
- Description: 2003000421
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
A method of truncated codifferential with application to some problems of cluster analysis
- Authors: Demyanov, Vladimir , Bagirov, Adil , Rubinov, Alex
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 23, no. 1 (May 2002), p. 63-80
- Full Text: false
- Reviewed:
- Description: A method of truncated codifferential descent for minimizing continuously codifferentiable functions is suggested. The convergence of the method is studied. Results of numerical experiments are presented. Application of the suggested method for the solution of some problems of cluster analysis are discussed. In numerical experiments Wisconsin Diagnostic Breast Cancer database was used.
- Description: 2003000062
Penalty functions with a small penalty parameter
- Authors: Rubinov, Alex , Yang, Xiao , Bagirov, Adil
- Date: 2002
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 17, no. 5 (2002), p. 931-964
- Full Text: false
- Reviewed:
- Description: In this article, we study the nonlinear penalization of a constrained optimization problem and show that the least exact penalty parameter of an equivalent parametric optimization problem can be diminished. We apply the theory of increasing positively homogeneous (IPH) functions so as to derive a simple formula for computing the least exact penalty parameter for the classical penalty function through perturbation function. We establish that various equivalent parametric reformulations of constrained optimization problems lead to reduction of exact penalty parameters. To construct a Lipschitz penalty function with a small exact penalty parameter for a Lipschitz programming problem, we make a transformation to the objective function by virtue of an increasing concave function. We present results of numerical experiments, which demonstrate that the Lipschitz penalty function with a small penalty parameter is more suitable for solving some nonconvex constrained problems than the classical penalty function.
- Description: 2003000116
A global optimisation approach to classification in medical diagnosis and prognosis
- Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John , Stranieri, Andrew
- Date: 2001
- Type: Text , Conference paper
- Relation: Paper presented at 34th Hawaii International Conference on System Sciences, HICSS-34, Maui, Hawaii, USA : 3rd-6th January 2001
- Full Text:
- Description: In this paper global optimisation-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with FNA image data from the Wisconsin Diagnostic and Prognostic Breast Cancer databases. First we discuss the problem of determining the most informative features for the classification of cancerous cases in the databases under consideration. Then we apply a technique based on convex and global optimisation to breast cancer diagnosis. It allows the classification of benign cases and malignant ones and the subsequent diagnosis of patients with very high accuracy. The third application of this technique is a method that calculates centres of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves higher accuracy with these databases than reported elsewhere in the literature.
- Description: 2003003950
Global optimization of marginal functions with applications to economic equilibrium
- Authors: Bagirov, Adil , Rubinov, Alex
- Date: 2001
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 20, no. 3-4 (Aug 2001), p. 215-237
- Full Text: false
- Reviewed:
- Description: We discuss the applicability of the cutting angle method to global minimization of marginal functions. The search of equilibrium prices in the exchange model can be reduced to the global minimization of certain functions, which include marginal functions. This problem has been approximately solved by the cutting angle method. Results of numerical experiments are presented and discussed.
Using global optimization to improve classification for medical diagnosis and prognosis
- Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John
- Date: 2001
- Type: Text , Journal article
- Relation: Topics in health information management Vol. 22, no. 1 (2001), p. 65-74
- Full Text: false
- Description: Global optimization-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with data from various databases. First, we discuss feature selection, the problem of determining the most informative features for classification in the databases under consideration. Then, we apply a technique based on convex and global optimization for classification in these databases. The third application of this technique is a method that calculates centers of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves high accuracy with these databases. Better classifiers will lead to improved assistance in making medical diagnostic and prognostic decisions.
- Description: 2003003662