A comparison of non-linear Lagrange and penalty functions for problems with a constraint
- Authors: Rubinov, Alex , Giri, Jason
- Date: 2001
- Type: Text , Conference paper
- Relation: Paper presented at 5th International Conference on Optimization: Techniques and Applications (ICOTA 2001), Hong Kong : 15th -17th December, 2001 p. 360-366
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003003929
A feature selection approach for unsupervised classification based on clustering
- Authors: Rubinov, Alex , Soukhoroukova, Nadejda , Ugon, Julien
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at Sixth International Conference on Optimization: Techniques and Applications (ICOTA) , University of Ballarat, Ballarat, Victoria : 9th-11th December 2004
- Full Text: false
- Description: Data have been collected for many years in different scientific (industrial, medical) research groups. Very often these groups kept all the the they could collect. It is possible that the data contains a lot of noisy features which do not bring any information, but make the problem more complicated. The additional study of eliminating non-informative and selecting informative features is very important in the area of Data Mining. There are several feature selection methods which were developed for supervised classification. The area of feature selection for unsupervised classification is not so developed. In this paper we present a new feature selection approach for unsupervised classification, based on clustering and nonsmooth optimisation techniques.
- Description: 2003004085
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
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- 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
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 lagrange penalty reformulation method for constrained optimization
- Authors: Rubinov, Alex , Yang, Xiao , Zhou, Y. Y.
- Date: 2007
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 1, no. 2 (2007), p. 145-154
- Full Text: false
- Reviewed:
- Description: In this paper a constrained optimization problem is transformed into an equivalent one in terms of an auxiliary penalty function. A Lagrange function method is then applied to this transformed problem. Zero duality gap and exact penalty results are obtained without any coercivity assumption on either the objective function or constraint functions. © 2006 Springer-Verlag.
- Description: C1
A lifetime measure for telecommunication network : Theoretical aspects
- Authors: Dzalilov, Zari , Rubinov, Alex , Ouveysi, Iradj
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at ICON 2003 - 2003 11th IEEE International Conference on Networks, Sydney : 28th September, 2003
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- Reviewed:
- Description: A new measure for network performance evaluation called topology lifetime was introduced in [Maxemchuk, N et al., May 2002], see also [Maxemchuk, N et al.]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach from [Maxemchuk, N et al., May 2002] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
- Description: E1
- Description: 2003000361
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
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.
A new algorithm for the placement of WLAN access point based on nonsmooth optimization technique
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the 7th International Conference on Advanced Communication Technology, Phoenix Park, Korea : 21st February, 2005
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- Reviewed:
- Description: In wireless local area network (WLAN), signal coverage is obtained by proper placement of access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they generate a coverage gap but if they are too close to each other, this leads to excessive co-channel interferences. In this paper, we describe a mathematical model we have developed to find the optimal number and location of APs. To solve the problem, we use an optimization algorithm developed at the University of Ballarat called discrete gradient algorithm. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
- Description: E1
- Description: 2003001376
Abstract convexity and augmented Lagrangians
- Authors: Burachik, Regina , Rubinov, Alex
- Date: 2007
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 18, no. 2 (2007), p. 413-436
- Full Text: false
- Reviewed:
- Description: The ultimate goal of this paper is to demonstrate that abstract convexity provides a natural language and a suitable framework for the examination of zero duality gap properties and exact multipliers of augmented Lagrangians. We study augmented Lagrangians in a very general setting and formulate the main definitions and facts describing the augmented Lagrangian theory in terms of abstract convexity tools. We illustrate our duality scheme with an application to stochastic semiinfinite optimization. © 2007 Society for Industrial and Applied Mathematics.
- Description: C1
- Description: 2003005362
Abstract convexity and non-smooth analysis : Global aspects
- Authors: Ioffe, A. D , Rubinov, Alex
- Date: 2002
- Type: Text , Journal article
- Relation: Advances in Mathematical Economics Vol. 4, no. (2002), p. 1-23
- Full Text: false
- Reviewed:
- Description: We study some types of convergence of abstract convex functions. We show that under certain conditions, convergence of support sets of a sequence of abstract convex functions implies graph convergence of the support sets at a point and the global subdifferential. Some examples and counterexamples are given.
- Description: C1
- Description: 2003000146
Abstract convexity for nonconvex optimization duality
- Authors: Nedic, A. , Ozdaglar, A. , Rubinov, Alex
- Date: 2007
- Type: Text , Journal article
- Relation: Optimization Vol. 56, no. 5-6 (2007), p. 655-674
- Full Text: false
- Reviewed:
- Description: In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.
- Description: C1
Abstract convexity of positive homogenous functions
- Authors: Rubinov, Alex , Dzalilov, Zari
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Statistics and Management Systems Vol. 5, no. 1 (2002), p. 1-19
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- Reviewed:
- Description: This paper is a survey of recent results to abstract convexity of positively homogeneous functions, that is, to a representation of such functions as the upper (lower) envelope of sets of fairly simple functions. In particular, we study sup-min and max-min representations of positively homogeneous of degree one functions through linear functions and various kinds of the so-called exhausters.
- Description: C1
- Description: 2003003353
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
An algorithm for monotonic global optimization problems
- Authors: Rubinov, Alex , Tuy, Hoang , Mays, Heather
- Date: 2001
- Type: Text , Journal article
- Relation: Optimization Vol. 49, no. 3 (2001), p. 205-221
- Full Text: false
- Reviewed:
- Description: We propose an algorithm to locate a global maximum of an increasing function subject to an increasing constraint on the cone of vectors with nonnegative coordinates. The algorithm is based on the outer approximation of the feasible set. We establish the convergence of the algorithm and provide a number of numerical experiments. We also discuss the types of constraints and objective functions for which the algorithm is best suited. © 2001 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.
An extended lifetime measure for telecommunication network
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 4, no. 2 (2008), p. 329-337
- Full Text:
- Reviewed:
- Description: A new measure for network performance evaluation called topology lifetime was introduced in [4, 5]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach of [4] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
Analysis of the Australian credit database
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the Symposium on Industrial Optimisation and the 9th Australian Optimisation Day, Perth : 30th September, 2002
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000353
Attracting sets for increasing co-radiant and topical operators
- Authors: Kloeden, Peter , Rubinov, Alex
- Date: 2002
- Type: Text , Journal article
- Relation: Mathematische Nachrichten Vol. 243, no. (2002), p. 134-145
- Full Text: false
- Reviewed:
- Description: A generalization of the Perron-Frobenius theorem to increasing positively homogeneous of degree one operators is extended to increasing co-radiant and topical operators, which are of interest in mathematical economics. In particular, small attracting sets containing the limit points of all sequences generated by iteration of such operators are determined.
- Description: C1
- Description: 2003000150
B-convex sets and functions
- Authors: Adilov, G. , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 27, no. 3-4 (Apr-May 2006), p. 237-257
- Full Text: false
- Reviewed:
- Description: A subset B of R-+(n) is B-convex if for all x, y is an element of B and all t is an element of [0, 1] one has max (tx, y) is an element of B. These sets were first investigated in [1, 2]. In this paper, we examine radiant B-convex sets and also introduce and study B-convex functions.
- Description: C1
- Description: 2003001836
Best approximation by downward sets with applications
- Authors: Rubinov, Alex , Mohebi, Hossein
- Date: 2006
- Type: Text , Journal article
- Relation: Analysis in Theory and Applications Vol. 22, no. 1 (2006), p. 20-40
- Full Text:
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- Description: We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.
- Description: C1
- Description: 2003001535