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Optimality conditions in nonconvex optimization via weak subdifferentials

- Kasimbeyli, Refail, Mammadov, Musa

  • Authors: Kasimbeyli, Refail , Mammadov, Musa
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Nonlinear Analysis, Theory, Methods and Applications Vol. 74, no. 7 (2011), p. 2534-2547
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  • Description: In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. © 2011 Elsevier Ltd. All rights reserved.

Workload coverage through nonsmooth optimization

- Sukhorukova, Nadezda, Ugon, Julien, Yearwood, John

  • Authors: Sukhorukova, Nadezda , Ugon, Julien , Yearwood, John
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 24, no. 2 (2009), p. 285-298
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  • Description: In this paper, workload coverage is the problem of identifying a pattern of days worked and days off, along with the number of hours worked on each work day. This pattern must satisfy certain work-related constraints and fit best to a predefined workload. In our study, we formulate the problem of workload coverage as an optimization problem. We propose a number of models which take into consideration various staffing constraints. For each of these models, our study aims to find a compromise between an accurate workload coverage and the ability to solve the corresponding optimization problems in a reasonable time. Numerical experiments on each model are carried out and the results are presented. Interestingly, the nonlinear programming approaches are found to be competitive with linear programming ones. © 2009 Taylor & Francis.

A filled function method for quadratic programs with binary constraints

- Wu, Zhiyou, Yang, Y. J., Bai, Fusheng

  • Authors: Wu, Zhiyou , Yang, Y. J. , Bai, Fusheng
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Optimization Vol. 58, no. 5 (2009), p. 585-598
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  • Description: In this article, we first introduce a definition of a local minimizer for the quadratic programs with {-1, 1} constraints and show that the existing necessary condition of global optimality in some recent literature is in fact the necessary and sufficient condition of local optimality under the present definition. A filled function and the corresponding filled function algorithm then are proposed to get the global minimizer of the concerned minimization problem. The existing sufficient condition of global optimality is employed to form one of the termination rules of the algorithm. Several numerical examples are reported to show the efficiency of the present method for solving quadratic programs with binary constraints.

Mathematical models for failure reconfiguration of telecommunication networks : Part 1

- Dzalilov, Zari, Ouveysi, Iradj

  • Authors: Dzalilov, Zari , Ouveysi, Iradj
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Optimization Vol. 58, no. 5 (2009), p. 483-504
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  • Description: This article proposes various mathematical modelling of networks for failure recovery. We consider a survivable communication network which is designed to carry different types of services under service level agreements (SLAs) between the network provider and the network users. Two different approaches for dynamical reconfiguration of networks are presented: with and without penalization. The approach without penalization does not require to consider the status of SLAs during the process of network reconfiguration. The second approach considers the status of the SLAs in the network and the corresponding re-optimization model for network reconfiguration is more complicated as the dimension of the linear programming problem in this case is higher than one for the problem of optimization without penalization. Some mathematical models and solution methodologies for this network operation problem are presented and an extensive implementation result has been provided.

Optimization based clustering algorithms in multicast group hierarchies

- Jia, Long, Ouveysi, Iradj, Rubinov, Alex, Bagirov, Adil

Integrated production system optimization using global optimization techniques

- Mason, T. L., Emelle, C., Van Berkel, J., Bagirov, Adil, Kampas, F., Pinter, J. D.

  • Authors: Mason, T. L. , Emelle, C. , Van Berkel, J. , Bagirov, Adil , Kampas, F. , Pinter, J. D.
  • Date: 2007
  • Type: Text , Journal article
  • Relation: Journal of Industrial and Management Optimization Vol. 3, no. 2 (May 2007), p. 257-277
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  • Description: Many optimization problems related to integrated oil and gas production systems are nonconvex and multimodal. Additionally, apart from the innate nonsmoothness of many optimization problems, nonsmooth functions such as minimum and maximum functions may be used to model flow/pressure controllers and cascade mass in the gas gathering and blending networks. In this paper we study the application of different versions of the derivative free Discrete Gradient Method (DGM) as well as the Lipschitz Global Optimizer (LGO) suite to production optimization in integrated oil and gas production systems and their comparison with various local and global solvers used with the General Algebraic Modeling System (GAMS). Four nonconvex and nonsmooth test cases were constructed from a small but realistic integrated gas production system optimization problem. The derivation of the system of equations for the various test cases is also presented. Results demonstrate that DGM is especially effective for solving nonsmooth optimization problems and its two versions are capable global optimization algorithms. We also demonstrate that LGO solves successfully the presented test (as well as other related real-world) problems.
  • Description: C1
  • Description: 2003004725

Improving risk grouping rules for prostate cancer patients with optimization

- Churilov, Leonid, Bagirov, Adil, Schwartz, Daniel, Smith, Kate, Dally, Michael

  • Authors: Churilov, Leonid , Bagirov, Adil , Schwartz, Daniel , Smith, Kate , Dally, Michael
  • Date: 2004
  • Type: Text , Conference paper
  • Relation: Paper presented at the 37th Annual Hawaii International Conference on System Sciences, Big Island, Hawaii : 5th January, 2004
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  • Description: Data mining techniques provide a popular and powerful toolset to address both clinical and management issues in the area of health care. This paper describes the study of assigning prostate cancer patients into homogenous groups with the aim to support future clinical treatment decisions. The cluster analysis based model is suggested and an application of non-smooth non-convex optimization techniques to solve this model is discussed. It is demonstrated that using the optimization based approach to data mining of a prostate cancer patients database can lead to generation of a significant amount of new knowledge that can be effectively utilized to enhance clinical decision making.
  • Description: E1
  • Description: 2003000846

The choice of a similarity measure with respect to its sensitivity to outliers

- Rubinov, Alex, Sukhorukova, Nadezda, Ugon, Julien

  • Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 709-721
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  • Description: This paper examines differences in the choice of similarity measures with respect to their sensitivity to outliers in clustering problems, formulated as mathematical programming problems. Namely, we are focusing on the study of norms (norm-based similarity measures) and convex functions of norms (function-norm-based similarity measures). The study consists of two parts: the study of theoretical models and numerical experiments. The main result of this study is a criterion for the outliers sensitivity with respect to the corresponding similarity measure. In particular, the obtained results show that the norm-based similarity measures are not sensitive to outliers whilst a very widely used square of the Euclidean norm similarity measure (least squares) is sensitive to outliers. Copyright © 2010 Watam Press.

Incremental DC optimization algorithm for large-scale clusterwise linear regression

- Bagirov, Adil, Taheri, Sona, Cimen, Emre

  • Authors: Bagirov, Adil , Taheri, Sona , Cimen, Emre
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Journal of Computational and Applied Mathematics Vol. 389, no. (2021), p. 1-17
  • Relation: https://purl.org/au-research/grants/arc/DP190100580
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  • Description: The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental approach is designed to solve the CLR problem. We apply the Quasi-Newton method to solve the subproblems. The proposed algorithm is evaluated using several synthetic and real-world data sets for regression and compared with other algorithms for CLR. Results demonstrate that the DCA based algorithm is efficient for solving CLR problems with the large number of data points and in particular, outperforms other algorithms when the number of input variables is small. © 2020 Elsevier B.V.

From convex to nonconvex: A loss function analysis for binary classification

- Zhao, Lei, Mammadov, Musa, Yearwood, John

  • Authors: Zhao, Lei , Mammadov, Musa , Yearwood, John
  • Date: 2010
  • Type: Text , Conference paper
  • Relation: Paper presented at10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 p. 1281-1288
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  • Description: Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ø-loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. © 2010 IEEE.

Optimization of parameters of the Kelvin element in vibration analysis

- Kuznetsov, Alexey, Mammadov, Musa, Hajilarov, Eldar

GOM: New Genetic Optimizing Model for broadcasting tree in MANET

- Elaiwat, Said, Alazab, Ammar, Venkatraman, Sitalakshmi, Alazab, Mamoun

  • Authors: Elaiwat, Said , Alazab, Ammar , Venkatraman, Sitalakshmi , Alazab, Mamoun
  • Date: 2010
  • Type: Text , Conference proceedings
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  • Description: Data broadcasting in a mobile ad-hoc network (MANET) is the main method of information dissemination in many applications, in particular for sending critical information to all hosts. Finding an optimal broadcast tree in such networks is a challenging task due to the broadcast storm problem. The aim of this work is to propose a new genetic model using a fitness function with the primary goal of finding an optimal broadcast tree. Our new method, called Genetic Optimisation Model (GOM) alleviates the broadcast storm problem to a great extent as the experimental simulations result in efficient broadcast tree with minimal flood and minimal hops. The result of this model also shows that it has the ability to give different optimal solutions according to the nature of the network. © 2010 IEEE.

Optimization of multiple classifiers in data mining based on string rewriting systems

- Dazeley, Richard, Kelarev, Andrei, Yearwood, John, Mammadov, Musa

Optimization of twin-screw extrusion process to produce okara-maize snack foods using response surface methodology

- Shi, Cong, Wang, Li-jun, Wu, Min, Adhikari, Benu, Li, Li-te

  • Authors: Shi, Cong , Wang, Li-jun , Wu, Min , Adhikari, Benu , Li, Li-te
  • Date: 2011
  • Type: Text , Journal article
  • Relation: International Journal of Food Engineering Vol. 7, no. 2 (2011), p.
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  • Description: Okara-maize flour blends were extruded in a co-rotating twin-screw extruder in order to assess their suitability as snack foods. Response surface methodology (RSM) using a central composite design was used to evaluate the effects of process variables (extrusion temperature (120-180 degrees C), screw speed (100-180 rpm) and feed composition (20-40 percent ww) and moisture content (14-22 percent ww)). Multiple regression equations were developed to describe the effects of each variable on product responses. The product characteristics such as bulk density, expansion index, appearance (colour, porosity), flavor (aroma, grittiness and off-odor), texture (hardness, crispness and brittleness) and overall acceptability were determined through experiments and sensory analyses. Through superimposed RSM contour map, it was found that the feed composition with 30 percent okara content, 14.5-19.3 percent moisture content and the extrusion temperature 120.0-171.2 degrees C and screw speed of 140 rpm, respectively to be the optimum extrusion conditions. The sensory tests showed that the products extruded at the optimized condition had the best appearance, taste, texture and overall acceptability. These results show that the okara-maize blends can be extruded into acceptable snack foods.

Optimization of back-propagation neural networks architecture and parameters with a hybrid PSO/SA approach

- Zarei, Mahdi, Dzalilov, Zari

Fast modified global k-means algorithm for incremental cluster construction

- Bagirov, Adil, Ugon, Julien, Webb, Dean

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 44, no. 4 (2011), p. 866-876
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • Description: The k-means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and are inefficient for solving clustering problems in large datasets. Recently, incremental approaches have been developed to resolve difficulties with the choice of starting points. The global k-means and the modified global k-means algorithms are based on such an approach. They iteratively add one cluster center at a time. Numerical experiments show that these algorithms considerably improve the k-means algorithm. However, they require storing the whole affinity matrix or computing this matrix at each iteration. This makes both algorithms time consuming and memory demanding for clustering even moderately large datasets. In this paper, a new version of the modified global k-means algorithm is proposed. We introduce an auxiliary cluster function to generate a set of starting points lying in different parts of the dataset. We exploit information gathered in previous iterations of the incremental algorithm to eliminate the need of computing or storing the whole affinity matrix and thereby to reduce computational effort and memory usage. Results of numerical experiments on six standard datasets demonstrate that the new algorithm is more efficient than the global and the modified global k-means algorithms. © 2010 Elsevier Ltd. All rights reserved.

Parameter optimization for Support Vector Machine Classifier with IO-GA

- Zhou, Jing, Maruatona, Omaru, Wang, Wei

  • Authors: Zhou, Jing , Maruatona, Omaru , Wang, Wei
  • Date: 2011
  • Type: Text , Conference proceedings
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  • Description: The Support Vector Machine method has a good learning and generalization ability. Unfortunately, there are no comprehensive theories to guide the parameter selection of the SVM, which largely limits its application. In order to get the optimal parameters automatically, researchers have tried a variety of methods. Using genetic algorithms to optimize parameters of an SVM Classifier has become one of the favorite methods in recent years. In this paper, we explain how the Standard Genetic Algorithm (SGA) causes the problem of premature convergence and limits the accuracy of the SVM. We also put forward a new genetic algorithm with improved genetic operators (IO-GA) to optimize the SVM classifier's parameters. Experimental results show that the parameters obtained by this method can greatly improve the classification performance of SVM. We therefore conclude that this method is effective. © 2011 IEEE.

A heuristic algorithm for solving the minimum sum-of-squares clustering problems

- Ordin, Burak, Bagirov, Adil

  • Authors: Ordin, Burak , Bagirov, Adil
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 61, no. 2 (2015), p. 341-361
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k-means and modified global k-means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global k-means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the k-means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global k-means algorithms in finding global solutions to clustering problems.

The effect of regularization on drug-reaction relationships

- Mammadov, Musa, Zhao, L., Zhang, Jianjun

  • 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.

An efficient classification using support vector machines

- Ruan, Ning, Chen, Yi, Gao, David

  • Authors: Ruan, Ning , Chen, Yi , Gao, David
  • Date: 2013
  • Type: Text , Conference paper
  • Relation: Proceedings of 2013 Science and Information Conference, SAI 2013 p. 585-589
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  • Description: Support vector machine (SVM) is a popular method for classification in data mining. The canonical duality theory provides a unified analytic solution to a wide range of discrete and continuous problems in global optimization. This paper presents a canonical duality approach for solving support vector machine problem. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to a unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2013 The Science and Information Organization.