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Lagrange-type functions in constrained optimization

- Rubinov, Alex, Yang, Xiao, Bagirov, Adil, Gasimov, Rafail

  • 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
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  • 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

Limited Memory Bundle Method for Clusterwise Linear Regression

- Karmitsa, Napsu, Bagirov, Adil, Taheri, Sona, Joki, Kaisa

  • Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona , Joki, Kaisa
  • Date: 2022
  • Type: Text , Book chapter
  • Relation: Intelligent Systems, Control and Automation: Science and Engineering p. 109-122
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: A clusterwise linear regression problem consists of finding a number of linear functions each approximating a subset of the given data. In this paper, the limited memory bundle method is modified and combined with the incremental approach to solve this problem using its nonsmooth optimization formulation. The main contribution of the proposed method is to obtain a fast solution time for large-scale clusterwise linear regression problems. The proposed algorithm is tested on small and large real-world data sets and compared with other algorithms for clusterwise linear regression. Numerical results demonstrate that the proposed algorithm is especially efficient in data sets with large numbers of data points and input variables. © 2022, Springer Nature Switzerland AG.

Determining regularization parameters for derivative free neural learning

- Ghosh, Ranadhir, Ghosh, Moumita, Yearwood, John, Bagirov, Adil

  • Authors: Ghosh, Ranadhir , Ghosh, Moumita , Yearwood, John , Bagirov, Adil
  • Date: 2005
  • Type: Text , Conference paper
  • Relation: Paper presented at 4th International Conference, MLDM 2005: Machine Learning and Data Mining in Pattern Recognition, Leipzig, Germany : 9th-11th July 2005 p. 71-79
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  • Description: Derivative free optimization methods have recently gained a lot of attractions for neural learning. The curse of dimensionality for the neural learning problem makes local optimization methods very attractive; however the error surface contains many local minima. Discrete gradient method is a special case of derivative free methods based on bundle methods and has the ability to jump over many local minima. There are two types of problems that are associated with this when local optimization methods are used for neural learning. The first type of problems is initial sensitivity dependence problem- that is commonly solved by using a hybrid model. Our early research has shown that discrete gradient method combining with other global methods such as evolutionary algorithm makes them even more attractive. These types of hybrid models have been studied by other researchers also. Another less mentioned problem is the problem of large weight values for the synaptic connections of the network. Large synaptic weight values often lead to the problem of paralysis and convergence problem especially when a hybrid model is used for fine tuning the learning task. In this paper we study and analyse the effect of different regularization parameters for our objective function to restrict the weight values without compromising the classification accuracy.
  • Description: 2003001362

A simulated annealing-based maximum-margin clustering algorithm

- Seifollahi, Sattar, Bagirov, Adil, Borzeshi, Ehsan, Piccardi, Massimo

  • Authors: Seifollahi, Sattar , Bagirov, Adil , Borzeshi, Ehsan , Piccardi, Massimo
  • Date: 2019
  • Type: Text , Journal article
  • Relation: Computational Intelligence Vol. 35, no. 1 (2019), p. 23-41
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  • Description: Maximum-margin clustering is an extension of the support vector machine (SVM) to clustering. It partitions a set of unlabeled data into multiple groups by finding hyperplanes with the largest margins. Although existing algorithms have shown promising results, there is no guarantee of convergence of these algorithms to global solutions due to the nonconvexity of the optimization problem. In this paper, we propose a simulated annealing-based algorithm that is able to mitigate the issue of local minima in the maximum-margin clustering problem. The novelty of our algorithm is twofold, ie, (i) it comprises a comprehensive cluster modification scheme based on simulated annealing, and (ii) it introduces a new approach based on the combination of k-means++ and SVM at each step of the annealing process. More precisely, k-means++ is initially applied to extract subsets of the data points. Then, an unsupervised SVM is applied to improve the clustering results. Experimental results on various benchmark data sets (of up to over a million points) give evidence that the proposed algorithm is more effective at solving the clustering problem than a number of popular clustering algorithms.

Alexander Rubinov - An outstanding scholar

- Bagirov, Adil

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.

Local optimization method with global multidimensional search

- Bagirov, Adil, Rubinov, Alex, Zhang, Jiapu

  • 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

Solving DC programs using the cutting angle method

- Ferrer, Albert, Bagirov, Adil, Beliakov, Gleb

The cutting angle method and its applications

- Bagirov, Adil

  • Authors: Bagirov, Adil
  • Date: 2001
  • Type: Text , Thesis , PhD
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  • Description: "The main objective of this thesis is to develop and study new techniques for solving global optimization problems and to apply them to solving data classification problems."

Nonsmooth optimization algorithm for solving clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

  • Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Optimization Theory and Applications Vol. 164, no. 3 (2015), p. 755-780
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: Clusterwise linear regression consists of finding a number of linear regression functions each approximating a subset of the data. In this paper, the clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem and an algorithm based on an incremental approach and on the discrete gradient method of nonsmooth optimization is designed to solve it. This algorithm incrementally divides the whole dataset into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate good starting points for solving global optimization problems at each iteration of the incremental algorithm. The algorithm is compared with the multi-start Spath and the incremental algorithms on several publicly available datasets for regression analysis.

Adaption to water shortage through the implementation of a unique pipeline system in Victoria, Australia

- Mala-Jetmarova, Helena, Barton, Andrew, Bagirov, Adil, McRae-Williams, Pamela, Caris, Rob, Jackson, Peter

  • Authors: Mala-Jetmarova, Helena , Barton, Andrew , Bagirov, Adil , McRae-Williams, Pamela , Caris, Rob , Jackson, Peter
  • Date: 2010
  • Type: Conference paper
  • Relation: Paper presented at Hydropredict' 2010, 2nd International Interdisciplinary Conference on predications for Hydrology, Ecology, and Water Resources Management
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  • Description: Abstract Water resource development has played a crucial role in the Grampians, Wimmera and Mallee regions of Australia, with the main source of surface water located in several reservoirs in the Grampians mountain ranges. Historically, water was delivered by gravity through a vast 19 500 km earthen channel system from the reservoirs to the townships and farms. As a result of the severe and protracted drought experienced in the region over the past 13 years and the projected drying climate, there have been fundamental changes made to the management of water in order to better cope with water scarcity. The primary strategic effort to sustainably manage water resources was by removing the unsustainable transport of water via the open channels which resulted in very high losses through seepage and evaporation. This inefficient system has been replaced by a pressurised pipeline, the largest geographical water infrastructure project of its type in Australia, spreading across an area of approximately 20 000 km2. To manage the change in water balance as a result of the pipeline and drying climate, the regions water corporations and environmental agencies have designed a scheme for water allocations intended to sustain local communities, allow for regional development and improve environmental conditions. This paper describes the unique pipeline system recently completed, provides a brief summary of water sharing arrangements and introduces the research program currently underway to optimise the performance of the pipeline system.

A method of truncated codifferential with application to some problems of cluster analysis

- Demyanov, Vladimir, Bagirov, Adil, Rubinov, Alex

  • Authors: Demyanov, Vladimir , Bagirov, Adil , Rubinov, Alex
  • Date: 2002
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 23, no. 1 (May 2002), p. 63-80
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  • Description: A method of truncated codifferential descent for minimizing continuously codifferentiable functions is suggested. The convergence of the method is studied. Results of numerical experiments are presented. Application of the suggested method for the solution of some problems of cluster analysis are discussed. In numerical experiments Wisconsin Diagnostic Breast Cancer database was used.
  • Description: 2003000062

Classification through incremental max-min separability

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

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Karasozen, Bulent
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Pattern Analysis and Applications Vol. 14, no. 2 (2011), p. 165-174
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • Description: Piecewise linear functions can be used to approximate non-linear decision boundaries between pattern classes. Piecewise linear boundaries are known to provide efficient real-time classifiers. However, they require a long training time. Finding piecewise linear boundaries between sets is a difficult optimization problem. Most approaches use heuristics to avoid solving this problem, which may lead to suboptimal piecewise linear boundaries. In this paper, we propose an algorithm for globally training hyperplanes using an incremental approach. Such an approach allows one to find a near global minimizer of the classification error function and to compute as few hyperplanes as needed for separating sets. We apply this algorithm for solving supervised data classification problems and report the results of numerical experiments on real-world data sets. These results demonstrate that the new algorithm requires a reasonable training time and its test set accuracy is consistently good on most data sets compared with mainstream classifiers. © 2010 Springer-Verlag London Limited.

An algorithm for minimizing clustering functions

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2005
  • Type: Text , Journal article
  • Relation: Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368
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  • Description: The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.
  • Description: C1
  • Description: 2003001266

A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes

- Joki, Kaisa, Bagirov, Adil, Karmitsa, Napsu, Makela, Marko

  • Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko
  • Date: 2017
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 68, no. 3 (2017), p. 501-535
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to utilize subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain a new nonconvex cutting plane model of the original objective function, which takes into account explicitly both the convex and the concave behavior of the objective function. We design the proximal bundle method for DC programming based on this new approach and prove the convergence of the method to an -critical point. The algorithm is tested using some academic test problems and the preliminary numerical results have shown the good performance of the new bundle method. An interesting fact is that the new algorithm finds nearly always the global solution in our test problems.

A quasisecant method for minimizing nonsmooth functions

- Bagirov, Adil, Ganjehlou, Asef Nazari

  • Authors: Bagirov, Adil , Ganjehlou, Asef Nazari
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 25, no. 1 (2010), p. 3-18
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
  • Full Text: false
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  • Description: We present an algorithm to locally minimize nonsmooth, nonconvex functions. In order to find descent directions, the notion of quasisecants, introduced in this paper, is applied. We prove that the algorithm converges to Clarke stationary points. Numerical results are presented demonstrating the applicability of the proposed algorithm to a wide variety of nonsmooth, nonconvex optimization problems. We also compare the proposed algorithm with the bundle method using numerical results.

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

  • Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
  • Date: 2013
  • Type: Text , Journal article
  • Relation: European Journal of Operational Research Vol. 229, no. 1 (2013), p. 132-142
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  • Description: Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis. © 2013 Elsevier B.V. All rights reserved.
  • Description: 2003011018

Modified self-organising maps with a new topology and initialisation algorithm

- Mohebi, Ehsan, Bagirov, Adil

  • Authors: Mohebi, Ehsan , Bagirov, Adil
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Experimental and Theoretical Artificial Intelligence Vol. 27, no. 3 (2015), p. 351-372
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  • Description: Mapping quality of the self-organising maps (SOMs) is sensitive to the map topology and initialisation of neurons. In this article, in order to improve the convergence of the SOM, an algorithm based on split and merge of clusters to initialise neurons is introduced. The initialisation algorithm speeds up the learning process in large high-dimensional data sets. We also develop a topology based on this initialisation to optimise the vector quantisation error and topology preservation of the SOMs. Such an approach allows to find more accurate data visualisation and consequently clustering problem. The numerical results on eight small-to-large real-world data sets are reported to demonstrate the performance of the proposed algorithm in the sense of vector quantisation, topology preservation and CPU time requirement. © 2014 Taylor & Francis.

Application of optimisation-based data mining techniques to tobacco control dataset

- Dzalilov, Zari, Zhang, J, Bagirov, Adil, Mammadov, Musa

  • Authors: Dzalilov, Zari , Zhang, J , Bagirov, Adil , Mammadov, Musa
  • Date: 2010
  • Type: Text , Journal article
  • Relation: International Journal of Lean Thinking Vol. 1, no. 1 (2010), p. 27-41
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  • Description: Tobacco smoking is one of the leading causes of death around the world. Consequently, control of tobacco use is an important global public health issue. Tobacco control may be aided by development of theoretical and methodological frameworks for describing and understanding complex tobacco control systems. Linear regression and logistic regression are currently very popular statistical techniques for modeling and analyzing complex data in tobacco control systems. However, in tobacco markets, numerous interrelated factors nontrivially interact with tobacco control policies, such that policies and control outcomes are nonlinearly related.

Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2006
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195
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  • Description: This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.
  • Description: 2003001532