The study of drug-reaction relationships using global optimization techniques
- Authors: Mammadov, Musa , Rubinov, Alex , Yearwood, John
- Date: 2007
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 22, no. 1 (2007), p. 99-126
- Full Text: false
- Reviewed:
- Description: In this paper we develop an optimization approach for the study of adverse drug reaction (ADR) problems. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although it can be used for solving many ADR problems, we concentrate on two of them here: the accurate identification of drugs that are responsible for reactions that have occurred, and drug-drug interactions. Based on drug-reaction relationships, we formulate these problems as an optimization problem. The approach is applied to cardiovascularn-type reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database. Software based on this approach has been developed and could have beneficial use in prescribing.
- Description: C1
- Description: 2003002217
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
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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
Best approximation in a class of normed spaces with star-shaped cone
- Authors: Mohebi, Hossein , Sadeghi, H. , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 27, no. 3-4 (Apr-May 2006), p. 411-436
- Full Text: false
- Reviewed:
- Description: We examine best approximation by closed sets in a class of normed spaces with star-shaped cones. It is assumed that the norm on the space X under consideration is generated by a star-shaped cone. First, we study best approximation by downward and upward sets, and then we use the results obtained as a tool for examination of best approximation by an arbitrary closed set.
- Description: C1
- Description: 2003001837
Classes and clusters in data analysis
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
- Date: 2006
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 173, no. 3 (Sep 2006), p. 849-865
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- Description: We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. (c) 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001593
Conical decomposition and vector lattices with respect to several preorders
- Authors: Baratov, Rishat , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Taiwanese Journal of Mathematics Vol. 10, no. 2 (2006), p. 265-298
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- Description: The decomposition set-valued mapping in a Banach space E with cones K i,i = 1,..., n describes all decompositions of a given element on addends, such that addend i belongs to the i-th cone. We examine the decomposition mapping and its dual. We study conditions that provide the additivity of the decomposition mapping. For this purpose we introduce and study the Riesz interpolation property and lattice properties of spaces with respect to several preorders. The notion of 2-vector lattice is introduced and studied. Theorems that establish the relationship between the Riesz interpolation property and lattice properties of the dual spaces are given.
- Description: C1
- Description: 2003001553
Coverage in WLAN : Optimization model and algorithm
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at the First International Conference on Wireless Broadband and Ultra Wideband Communications, AusWireless 2006, Sydney : 13th March, 2006
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- Description: When designing wireless communication systems, it is very important to know the optimum numbers of access points (APs) in order to provide a reliable design. In this paper we describe a mathematical model developed for finding the optimal number and location of APs. A new Global Optimization Algorithm (AGOP) is used to solve the problem. Results obtained demonstrate that the model and software are able to solve optimal coverage problems for design areas with different types of obstacles and number of users.
- Description: 2003001757
Coverage in WLAN with minimum number of access points
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Rubinov, Alex , Kruger, Alexander , Mammadov, Musa
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at VTC 2006 - Spring, 2006 IEEE 63rd Vehicular Technology Conference, Melbourne : 7th May, 2006
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- Description: E1
- Description: 2003001610
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
Metric projection onto a closed set : Necessary and sufficient conditions for the global minimum
- Authors: Mohebi, Hossein , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Mathematics of Operations Research Vol. 31, no. 1 (2006), p. 124-132
- Full Text: false
- Reviewed:
- Description: Necessary and sufficient conditions for a local minimum form a well-developed chapter of optimization theory. Determination of such conditions for the global minimum is a challenging problem. Useful conditions are currently known only for a few classes of nonconvex optimization problems. It is important to find different classes of problems for which the required conditions can be obtained. In this paper we examine one of these classes: the minimization of the distance to an arbitrary closed set in a class of ordered normed spaces. We use the structure of the objective function in order to present necessary and sufficient conditions that give a clear understanding of the structure of a global minimizer and can be easily verified for some problems under consideration. © 2006 INFORMS.
- Description: C1
- Description: 2003001835
Optimization in data mining
- Authors: Karasozen, Bulent , Rubinov, Alex , Weber, Gerhard-Wilhelm
- Date: 2006
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 173, no. 3 (2006), p. 701-704
- Full Text: false
- Reviewed:
- Description: C1
Star-shaped separability with applications
- Authors: Rubinov, Alex , Sharikov, Evgenii
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 13, no. 3-4 (2006), p. 849-860
- Full Text:
- Reviewed:
- Description: We discuss the notion of a support collection to a star-shaped set at a certain boundary point and a weak separability of two star-shaped sets. Applications to some problems, including the minimization of a star-shaped distance, are given. © Heldermann Verlag.
- Description: C1
- Description: 2003001592
Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints
- Authors: Jeyakumar, Vaithilingam , Rubinov, Alex , Wu, Zhiyou
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 36, no. 3 (2006), p. 471-481
- Full Text: false
- Reviewed:
- Description: In this paper we establish conditions which ensure that a feasible point is a global minimizer of a quadratic minimization problem subject to box constraints or binary constraints. In particular, we show that our conditions provide a complete characterization of global optimality for non-convex weighted least squares minimization problems. We present a new approach which makes use of a global subdifferential. It is formed by a set of functions which are not necessarily linear functions, and it enjoys explicit descriptions for quadratic functions. We also provide numerical examples to illustrate our optimality conditions.
- Description: C1
- Description: 2003001538
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
Dynamical systems described by relational elasticities with applications to global optimization
- Authors: Mammadov, Musa , Rubinov, Alex , Yearwood, John
- Date: 2005
- Type: Text , Book chapter
- Relation: Continuous Optimization: Current Trends and Modern Applications Chapter p. 365-385
- Full Text: false
- Reviewed:
- Description: B1
Hidden abstract convex functions
- Authors: Rubinov, Alex , Wu, Zhiyou , Li, Duan
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Nonlinear and Convex Analysis Vol. 6, no. 1 (2005), p. 203-216
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001424
Increasing quasiconcave co-radiant functions with applications in mathematical economics
- Authors: Martinez-Legaz, Juan , Rubinov, Alex , Schaible, Siegfried
- Date: 2005
- Type: Text , Journal article
- Relation: Mathematical Methods of Operations Research Vol. 61, no. 2 (2005), p. 261-280
- Full Text: false
- Reviewed:
- Description: We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In particular we identify a small "natural" infimal generator of the set of all coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of production functions and utility functions are discussed. © Springer-Verlag 2005.
- Description: C1
- Description: 2003001423
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
Minimization of the sum of minima of convex functions and its application to clustering
- Authors: Rubinov, Alex , Soukhoroukova, Nadejda , Ugon, Julien
- Date: 2005
- Type: Text , Book chapter
- Relation: Continuous Optimization Chapter p. 409-434
- Full Text:
- Description: We study functions that can be represented as the sum of minima of convex functions. Minimization of such functions can be used for approximation of finite sets and their clustering. We suggest to use the local discrete gradient (DG) method [Bag99] and the hybrid method between the cutting angle method and the discrete gradient method (DG+CAM) [BRZ05b] for the minimization of these functions. We report and analyze the results of numerical experiments.
- Description: 2003004082
Multipliers and general Lagrangians
- Authors: Penot, Jean Paul , Rubinov, Alex
- Date: 2005
- Type: Text , Journal article
- Relation: Optimization Vol. 54, no. 4-5 (2005), p. 443-467
- Full Text: false
- Reviewed:
- Description: We combine a Lagrangian approach inspired by convex and quasiconvex dualities with a penalization approach to mathematical programming. We use the ideas of abstract convexity. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as elements of generalized subdifferentials of the performance function associated with a dualizing parameterization of the given problem. © 2005 Taylor & Francis Group Ltd.
- Description: C1
- Description: 2003001422