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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- 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
Online LIB problems : Heuristics for bin covering and lower bounds for bin packing
- Authors: Finlay, L. , Manyem, Prabhu
- Date: 2005
- Type: Text , Journal article
- Relation: Rairo-Operations Research Vol. 39, no. 3 (Jul-Sep 2005), p. 163-183
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- Description: We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items - we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upper bounds. For variable sized bin covering, a more thorough analysis revealed definite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform size bins, no heuristic can guarantee an approximation ratio better than 1.76 under the online model considered.
- Description: C1
- Description: 2003001388
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
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
An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization
- Authors: Bagirov, Adil , Ganjehlou, Asef Nazari
- Date: 2008
- Type: Text , Journal article
- Relation: Mathematical Methods of Operations Research Vol. 67, no. 2 (2008), p. 187-206
- Relation: http://purl.org/au-research/grants/arc/DP0666061
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- Description: In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method. © 2007 Springer-Verlag.
- Description: C1
Implementation of lean manufacturing through learning curve modelling for labour forecast
- Authors: Gunawan, Indra
- Date: 2009
- Type: Text , Journal article
- Relation: International Journal of Mechanical & Mechatronics Engineering Vol. 9, no. 10 (2009), p. 46-52
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- Description: In this paper, an implementation of lean manufacturing through learning curve modelling for labour forecast is discussed. First, various learning curve models are presented. Then the models are analyzed in terms of their advantages and limitations. As a case study, the learning curve modelling is presented with the data derived from a production company. With the application of the learning curve, labour need can be more accurately predicted and scheduled on time.
New largest known graphs of diameter 6
- Authors: Pineda-Villavicencio, Guillermo , Gómez, José , Miller, Mirka , Pérez-Rosés, Hebert
- Date: 2009
- Type: Text , Journal article
- Relation: Networks Vol. 53, no. 4 (2009), p. 315-328
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- Description: In the pursuit of obtaining largest graphs of given maximum degree
- Description: 2003007890
Stability of error bounds for convex constraints systems in Banach spaces
- Authors: Thera, Michel , Van Ngai, Huynh , Kruger, Alexander
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 6 (2010), p. 3280-3296
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- Description: This paper studies stability of error bounds for convex constraints in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.
- Description: C1
Stability of error bounds for semi-infinite convex constraint systems
- Authors: Van Ngai, Huynh , Kruger, Alexander , Théra, Michel
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 4 (2010), p. 2080-2096
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- Description: In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its "small" perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Azé and Corvellec [SIAM J. Optim., 12 (2002), pp. 913-927] on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems. Copyright © 2010, Society for Industrial and Applied Mathematics.
Global asymptotic stability in a class of nonlinear differential delay equations
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.
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- Description: An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.
- Description: 2003009358
A new method for solving linear ill-posed problems
- Authors: Zhang, Jianjun , Mammadov, Musa
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 20 (2012), p.10180-10187
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- Description: In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush-Kuhn-Tucker conditions, Fisher-Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the proposed method is effective and promising for many practical problems. © 2012.
An extended lifetime measure for telecommunications networks : Improvements and implementations
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Bektas, Tolga
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 3 (2012), p. 639-649
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- Description: Predicting the lifetime of a network is a stochastic and very hard task. Sensitivity analysis of a network in order to identify the weakest points in the network, provides valuable knowledge to draw an optimum investment strategy for the expansion of the networks for the network carriers. To achieve this goal, a new measure, called topology lifetime, was recently proposed for measuring the performance of a telecommunication network. This measure not only allows to perform a sensitivity analysis of the networks, but also it provides the means to compare the different topologies with respect to the ability of the network in supporting growth in network traffic before new capacity/facility is installed. This paper addresses some improvements upon the previously defined measures and presents the implementation results of the various lifetime measure methodologies. Computational analysis on some commonly used topologies show how the new measure can be utilized in assessing network performance.
- Description: 2003010401
Comments on : Stability in linear optimization and related topics. A personal tour
- Authors: Kruger, Alexander
- Date: 2012
- Type: Text , Journal article
- Relation: TOP Vol. 20, no. 2 (2012), p. 255-257
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- Description: The article presents a report on a wonderful tour in the area of stability analysis of linear (and not only linear) optimization undertaken in the last 15 years by the author and his team of collaborators. 15 years is a very short period for developing a mathematical theory. Nevertheless the scope of achievement presented in the article and the level of development of the theory are really impressive. The tour is full of attractions and the route is very carefully marked. Now the tour is on offer, and the author is eager to share its highlights with interested travelers.
On Hölder calmness of solution mappings in parametric equilibrium problems
- Authors: Anh, Lam Quoc , Kruger, Alexander , Thao, Nguyen
- Date: 2012
- Type: Text , Journal article
- Relation: TOP Vol. 22, no. 1 (2012), p. 331-342
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- Description: We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces.
Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems
- Authors: Cánovas, Maria , López, Marco , Mordukhovich, Borris , Parra, Juan
- Date: 2012
- Type: Text , Journal article
- Relation: TOP Vol. 20, no. 2 (2012), p. 310-327
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system's data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504-1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system's coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.
Some remarks on stability of generalized equations
- Authors: Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 159, no. 3 (2012), p. 681-697
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian-Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided. © 2012 Springer Science+Business Media, LLC.
Stationarity and regularity of infinite collections of sets
- Authors: Kruger, Alexander , López, Marco
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 154, no. 2 (2012), p. 339-369
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: This article investigates extremality, stationarity, and regularity properties of infinite collections of sets in Banach spaces. Our approach strongly relies on the machinery developed for finite collections. When dealing with an infinite collection of sets, we examine the behavior of its finite subcollections. This allows us to establish certain primal-dual relationships between the stationarity/regularity properties some of which can be interpreted as extensions of the Extremal principle. Stationarity criteria developed in the article are applied to proving intersection rules for Fréchet normals to infinite intersections of sets in Asplund spaces. © 2012 Springer Science+Business Media, LLC.
Stationarity and Regularity of Infinite Collections of Sets. Applications to Infinitely Constrained Optimization
- Authors: Kruger, Alexander , López, Marco
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 155, no. 2 (2012), p. 390-416
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements-normals and/or subdifferentials.
Sufficient conditions for global optimality of semidefinite optimization
- Authors: Quan, Jing , Wu, Zhiyou , Li, Guoquan , Wu, Ou
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Inequalities and Applications Vol. 2012, no. 108
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- Description: In this article, by using the Lagrangian function, we investigate the sufficient global optimality conditions for a class of semi-definite optimization problems, where the objective function are general nonlinear, the variables are mixed integers subject to linear matrix inequalities (LMIs) constraints as well as bounded constraints. In addition, the sufficient global optimality conditions for general nonlinear programming problems are derived, where the variables satisfy LMIs constraints and box constraints or bivalent constraints. Furthermore, we give the sufficient global optimality conditions for standard semi-definite programming problem, where the objective function is linear, the variables satisfy linear inequalities constraints and box constraints. © 2012 Quan et al.
The effect of regularization on drug-reaction relationships
- Authors: Mammadov, Musa , Zhao, L. , Zhang, Jianjun
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 4 (2012), p. 405-422
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- Description: The least-squares method is a standard approach used in data fitting that has important applications in many areas in science and engineering including many finance problems. In the case when the problem under consideration involves large-scale sparse matrices regularization methods are used to obtain more stable solutions by relaxing the data fitting. In this article, a new regularization algorithm is introduced based on the Karush-Kuhn-Tucker conditions and the Fisher-Burmeister function. The Newton method is used for solving corresponding systems of equations. The advantages of the proposed method has been demonstrated in the establishment of drug-reaction relationships based on the Australian Adverse Drug Reaction Advisory Committee database. © 2012 Copyright Taylor and Francis Group, LLC.