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.
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
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- 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
Dynamic reconfiguration of telecommunication networks
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the Industrial Optimisation 2003 Conference, Perth : 30th October, 2002
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000451
On augmented lagrangians for optimization problems with a single constraint
- Authors: Gasimov, Rafail , Rubinov, Alex
- Date: 2004
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 28, no. 2 (2004), p. 153-173
- Full Text: false
- Reviewed:
- Description: We examine augmented Lagrangians for optimization problems with a single (either inequality or equality) constraint. We establish some links between augmented Lagrangians and Lagrange-type functions and propose a new kind of Lagrange-type functions for a problem with a single inequality constraint. Finally, we discuss a supergradient algorithm for calculating optimal values of dual problems corresponding to some class of augmented Lagrangians.
- Description: C1
- Description: 2003000929
Vector optimization problems with nonconvex preferences
- Authors: Huang, N. J. , Rubinov, Alex , Yang, Xiao
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 40, no. 4 (2008), p. 765-777
- Full Text: false
- Reviewed:
- Description: In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of vector complementarity problems, vector variational inequalities, and minimal element problems are also given. © 2007 Springer Science+Business Media, Inc.
- Description: C1
Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions
- Authors: Jeyakumar, Vaithilingam , Rubinov, Alex , Wu, Zhiyou
- Date: 2007
- Type: Text , Journal article
- Relation: Mathematical Programming Vol. 110, no. 3 (2007), p. 521-541
- Full Text: false
- Reviewed:
- Description: In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least squares with ellipsoidal constraints, and quadratic minimization with binary constraints. We discuss examples which demonstrate that our optimality conditions can effectively be used for identifying global minimizers of certain multi-extremal non-convex quadratic optimization problems. © Springer-Verlag 2007.
- Description: C1
Optimization in telecommunication network maintenance
- Authors: Jia, Long , Rubinov, Alex , Ouveysi, Iradj
- 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: 2003000349
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
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
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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- Reviewed:
- 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
Optimization in wireless local area network
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
- Reviewed:
- Description: 2003000886
Lagrange-type functions in constrained non-convex optimization
- Authors: Rubinov, Alex , Yang, Xiao
- Date: 2003
- Type: Text , Book
- Full Text: false
- Reviewed:
- Description: A1
- Description: 2003000355
The zero duality gap property and lower semicontinuity of the perturbation function
- Authors: Rubinov, Alex , Huang, X. X. , Yang, Xiao
- Date: 2002
- Type: Text , Journal article
- Relation: Mathematics of Operations Research Vol. 27, no. 4 (2002), p. 775-791
- Full Text: false
- Reviewed:
- Description: We examine the validity of the zero duality gap properties for two important dual schemes: a generalized augmented Lagrangian dual scheme and a nonlinear Lagrange-type dual scheme. The necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions.
- Description: 2003000117
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
- Full Text:
- 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
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
Sigma-porosity in monotonic analysis with applications to optimization
- Authors: Rubinov, Alex
- Date: 2005
- Type: Text , Journal article
- Relation: Abstract and Applied Analysis Vol. 2005, no. 3 (2005), p. 287-305
- Full Text: false
- Reviewed:
- Description: We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $sigma$-porous in corresponding spaces. Some applications to optimization are given.
- Description: C1
- Description: We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $\sigma$-porous in corresponding spaces. Some applications to optimization are given.
- Description: 2003001421
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
Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation
- Authors: Rubinov, Alex , Gasimov, Rafail
- Date: 2004
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 29, no. 4 (2004), p. 455-477
- Full Text: false
- Reviewed:
- Description: We consider problems of vector optimization with preferences that are not necessarily a pre-order relation. We introduce the class of functions which can serve for a scalarization of these problems and consider a scalar duality based on recently developed methods for non-linear penalization scalar problems with a single constraint.
- Description: C1
- Description: 2003000932
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