Difference inclusions with delay of economic growth
- Authors: Dzalilov, Zari , Ivanov, Anatoli , Rubinov, Alex
- Date: 2001
- Type: Text , Journal article
- Relation: Dynamic Systems and Applications Vol. 10 , no. (2001), p. 283-293
- Full Text: false
- Reviewed:
- Description: A difference inclusion wit.h delay is proposed as a modified model of maeroe<.'onomical growth. The classical assumpt.ion of t.he homogeneity of the nonlinear feedback involved in the model implies t.he existence of a ray of equilibria. Any dynamics in the model is shown to be convergent. t.o either an equilibrium on the ray or to the zero equilibrium.
- Description: C1
- Description: 2003002561
Equilibrium with fixed budgets and superlinear connections
- Authors: Rubinov, Alex , Glover, Barney
- Date: 2001
- Type: Text , Journal article
- Relation: ANZIAM Journal Vol. 42, no. 4 (2001), p. 462-480
- Full Text: false
- Reviewed:
- Description: We study models of economic equilibrium with fixed budgets and assuming superlinear connections between consumption and production. Extremal problems and the existence of equilibria are discussed for such models along with some related differential properties. Examples to illustrate the broad nature of the model are discussed. © Australian Mathematical Society 2001.
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
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
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
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
Stability of semi-infinite inequality systems involving min-type functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 81-112
- Full Text: false
- Reviewed:
- Description: We study the stability of semi-infinite inequality systems that arise in monotonic analysis. These systems are defined by certain classes of abstract linear functions. We consider the cone R
- Description: C1
- Description: 2003001420
Stability of the lower level sets of ICAR functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 113-127
- Full Text: false
- Reviewed:
- Description: In this paper, we study the stability of the lower level set {x E R++n | f (x) ≤ 0} of a finite valued increasing convex-along-rays (ICAR) function f defined on R++n. In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of R ++n. The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. Copyright © Taylor & Francis, Inc.
- Description: C1
- Description: 2003001419
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 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
- Full Text:
- Reviewed:
- 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
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
Facility location via continuous optimization with discontinuous objective functions
- Authors: Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2007
- Type: Text , Journal article
- Relation: ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325
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- Description: Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.
- Description: 2003004859
Global optimality conditions for some classes of optimization problems
- Authors: Wu, Zhiyou , Rubinov, Alex
- Date: 2009
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 145, no. 1 (2009), p. 164-185
- Full Text: false
- Reviewed:
- Description: We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract convexity. © 2009 Springer Science+Business Media, LLC.