Your selections:

33Gao, David
12Ruan, Ning
9Rubinov, Alex
8Bagirov, Adil
8Mammadov, Musa
7Wu, Zhiyou
5Ugon, Julien
5Zhou, Xiaojun
3Bai, Fusheng
3Chen, Yi
3Yang, Chunhua
3Yang, Yongjian
3Yearwood, John
3Zhang, Jiapu
3Zhu, Jinghao
2Banerjee, Arunava
2Beliakov, Gleb
2Dzalilov, Zari
2Fang, Shucherng
2Hanoun, Samer

Show More

Show Less

240103 Numerical and Computational Mathematics
200102 Applied Mathematics
13Canonical duality theory
90802 Computation Theory and Mathematics
8Canonical duality theories
8Problem solving
7Optimization
6Algorithms
5Canonical duality
5Integer programming
4Dual problem
4Maximization problem
4Perturbation method
301 Mathematical Sciences
3Convex set
3Data mining
3Dual transformation
3Duality theory
3Filled function

Show More

Show Less

Format Type

Advances in canonical duality theory with applications to global optimization

**Authors:**Gao, David**Date:**2008**Type:**Text , Conference proceedings**Relation:**FOCAPO 2008, Boston, June 29th-July 02, Published in Proceedings of the Fifth International Conference Foundations of Computer-Aided Process Operations pg. 73-82 p. 73-81**Full Text:**false**Reviewed:**

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**Full Text:**false**Reviewed:****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.

**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**Full Text:**false**Reviewed:****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.

H-infinity via a nonsmooth, nonconvex optimization approach

- Mammadov, Musa, Orsi, Robert

**Authors:**Mammadov, Musa , Orsi, Robert**Date:**2005**Type:**Text , Journal article**Relation:**Pacific Journal of Optimization Vol. 1, no. 2 (2005), p. 405-420**Full Text:**false**Reviewed:****Description:**A numerical method for solving the H-infinity synthesis problem is presented. The problem is posed as an unconstrained, nonsmooth, nonconvex minimization problem. The optimization variables consist solely of the entries of the output feedback matrix. No additional variables, such as Lyapunov variables, need to be introduced. The main part of the optimization procedure uses a line search mechanism where the descent direction is defined by a recently introduced dynamical systems approach. Numerical results for various benchmark problems are included in the paper. In addition, the effectiveness of a preliminary part of the algorithm for successfully and quickly finding stabilizing controllers is also demonstrated.**Description:**C1**Description:**2003001382

An optimization approach to the study of drug-drug interactions

- Mammadov, Musa, Banerjee, Arunava

**Authors:**Mammadov, Musa , Banerjee, Arunava**Date:**2005**Type:**Text , Conference paper**Relation:**Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 201-216**Full Text:****Description:**Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database.**Description:**2003001384

**Authors:**Mammadov, Musa , Banerjee, Arunava**Date:**2005**Type:**Text , Conference paper**Relation:**Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 201-216**Full Text:****Description:**Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database.**Description:**2003001384

An interesting cryptography study based on knapsack problem

**Authors:**Ruan, Ning**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings - UKSim 15th International Conference on Computer Modelling and Simulation, UKSim 2013 p. 330-334**Full Text:****Reviewed:****Description:**Cryptography is an art that has been practised through the centuries. Interest in the applications of the knapsack problem to cryptography has arisen with the advent of public key cryptography. The knapsack problem is well documented problem and all research into its properties have lead to the conjecture that it is difficult to solve. In this paper the canonical duality theory is presented for solving general knapsack problem. By using the canonical dual transformation, the integer programming problem can be converted into a continuous canonical dual problem with zero duality gap. The optimality criterion are also discussed. Numerical examples show the efficiency of the method. Â© 2013 IEEE.

**Authors:**Ruan, Ning**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings - UKSim 15th International Conference on Computer Modelling and Simulation, UKSim 2013 p. 330-334**Full Text:****Reviewed:****Description:**Cryptography is an art that has been practised through the centuries. Interest in the applications of the knapsack problem to cryptography has arisen with the advent of public key cryptography. The knapsack problem is well documented problem and all research into its properties have lead to the conjecture that it is difficult to solve. In this paper the canonical duality theory is presented for solving general knapsack problem. By using the canonical dual transformation, the integer programming problem can be converted into a continuous canonical dual problem with zero duality gap. The optimality criterion are also discussed. Numerical examples show the efficiency of the method. Â© 2013 IEEE.

Facility location via continuous optimization with discontinuous objective functions

- Ugon, Julien, Kouhbor, Shahnaz, Mammadov, Musa, Rubinov, Alex, Kruger, Alexander

**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**Full Text:****Reviewed:****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

**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**Full Text:****Reviewed:****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 optimization approach to identifying drugs responsible for adverse drug reactions

- Mammadov, Musa, Banerjee, Arunava

**Authors:**Mammadov, Musa , Banerjee, Arunava**Date:**2005**Type:**Text , Conference paper**Relation:**Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 185-200**Full Text:**false**Description:**In this paper we develop an optimization approach for the study of Adverse Drug Reaction (ADR) problems. This approach is based on drug-reaction relationships represented in the form of a vector weights, which can be defined as a solution to some global optimization problem. Although it can be used for solving many ADR problems, we concentrate on the problem of accurate identification of drugs that are responsible for reactions that have occurred. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to Australian Adverse Drug Reaction Advisory Committee (ADRAC) database. We take a comprehensive approach to considering all reaction classes which combines 18 SOC (System Organ Class), as well as the sub-classes of reaction classes Blood, Body, Neurological and Cardiovascular. The numerical experiments provided high accuracy in prediction of suspected drugs reported in ADRAC database.**Description:**2003001383

Cluster analysis of a tobacco control data set

- Dzalilov, Zari, Bagirov, Adil

**Authors:**Dzalilov, Zari , Bagirov, Adil**Date:**2010**Type:**Text , Journal article**Relation:**International Journal of Lean Thinking Vol. 1, no. 2 (2010), p.**Full Text:**false**Reviewed:****Description:**Development of theoretical and methodological frameworks in data analysis is fundamental for modeling complex tobacco control systems. Following this idea, a new optimization based approach was introduced in the paper through two distinct methods: the modified linear least square fit and a heuristic algorithm for feature slection based on optimization-based methods have the potential to detect nonlinearity, and therefore to be more effective analysis tools of complex data set. In this study we evaluate the modified global k-means clustering algorithm by applying it to a massive set of real-time tobacco control survey data. Cluster analysis identified fixed and stable clusters in the studied data. These clusters correspond to groups of smokers with similar behaviour and the identification of these clusters may allow us to give recommendations on modification of existing tobacco control systems and on the design of future data acquistion surveys.

Global optimal solutions to nonconvex euclidean distance geometry problems

**Authors:**Ruan, Ning , Gao, David**Date:**2012**Type:**Text , Conference paper**Relation:**20th International Symposium on Mathematical Theory of Networks and Systems**Full Text:**false**Reviewed:****Description:**This paper presents a canonical dual approach for solving nonconvex minimization problems in Euclidean distance geometry. The variant of this problem arises extensively in engineering and science, including computational biology, sensor network communications, database analysis, information technology, and global optimization. Due to the nonconvexity, most of these problems are NP-hard and traditional convex optimization methods can not be used directly for finding global optimal solutions. We first show that this type of nonconvex problems can be transferred to a concave maximization problem over a convex set. Then a general analytical solution is proposed by using the canonical duality theory. Applications are illustrated by network localization and minimization of Rosenbrock function. Furthermore, by using a perturbed canonical dual approach, a class of Euclidean distance problems can be converted to a unified concave maximization dual problem with zero duality gap, which can be solved by well-developed convex minimization methods.

Optimization solvers and problem formulations for solving data clustering problems

**Authors:**Ugon, Julien**Date:**2007**Type:**Text , Journal article**Relation:**Pacific Journal of Optimization Vol. 3, no. 2 (2007), p. 387-397**Full Text:**false**Reviewed:****Description:**A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.**Description:**C1**Description:**2003004937

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**Full Text:**false**Reviewed:****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.

Global optimum design of uniform FIR filter bank with magnitude constraints

- Wu, Changzhi, Teo, Kok Lay, Rehbock, Volker, Dam, Haihuyen

**Authors:**Wu, Changzhi , Teo, Kok Lay , Rehbock, Volker , Dam, Haihuyen**Date:**2008**Type:**Text , Journal article**Relation:**IEEE Transactions on Signal Processing Vol. 56, no. 11 (2008), p. 5478-5486**Full Text:**false**Reviewed:****Description:**The optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi-infinite optimization problem. However, this optimization problem is nonconvex with infinitely many inequality constraints. In this paper, we propose a new hybrid approach for solving this highly challenging nonlinear, nonconvex semi-infinite optimization problem. In this approach, a gradient-based method is used in conjunction with a filled function method to determine a global minimum of the problem. This new hybrid approach finds an optimal result independent of the initial guess of the solution. The method is applied to some existing examples. The results obtained are superior to those obtained by other existing methods. © 2008 IEEE.

Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems

- Zhou, Xiaojun, Gao, David, Yang, Chunhua

**Authors:**Zhou, Xiaojun , Gao, David , Yang, Chunhua**Date:**2014**Type:**Text , Journal article**Relation:**Applied Mathematics and Computation Vol. 227, no. (2014), p. 246-255**Full Text:**false**Reviewed:****Description:**This paper focuses on implementation of a general canonical primal-dual algorithm for solving a class of fourth-order polynomial minimization problems. A critical issue in the canonical duality theory has been addressed, i.e., in the case that the canonical dual problem has no interior critical point in its feasible space Sa+, a quadratic perturbation method is introduced to recover the global solution through a primal-dual iterative approach, and a gradient-based method is further used to refine the solution. A series of test problems, including the benchmark polynomials and several instances of the sensor network localization problems, have been used to testify the effectiveness of the proposed algorithm. © 2013 Published by Elsevier Inc. All rights reserved.

Canonical dual solutions for fixed cost quadratic programs

- Gao, David, Ruan, Ning, Sherali, Hanif

**Authors:**Gao, David , Ruan, Ning , Sherali, Hanif**Date:**2010**Type:**Text , Book chapter**Relation:**Optimization and Optimal Control p. 139-156**Full Text:**false**Reviewed:****Description:**This chapter presents a canonical dual approach for solving a mixed-integer quadratic minimization problem with fixed cost terms. We show that this well-known NP-hard problem in R2n can be transformed into a continuous concave maximization dual problem over a convex feasible subset of R2n with zero duality gap. The resulting canonical dual problem can be solved easily, under certain conditions, by traditional convex programming methods. Both existence and uniqueness of global optimal solutions are discussed. Application to a decoupled mixed-integer problem is illustrated and analytic solutions for both a global minimizer and a global maximizer are obtained. Examples for both decoupled and general nonconvex problems are presented. Furthermore, we discuss connections between the proposed canonical duality theory approach and the classical Lagrangian duality approach. An open problem is proposed for future study.

- Huda, Shamsul, Abdollahian, Mali, Mammadov, Musa, Yearwood, John, Ahmed, Shafiq, Sultan, Ibrahim

**Authors:**Huda, Shamsul , Abdollahian, Mali , Mammadov, Musa , Yearwood, John , Ahmed, Shafiq , Sultan, Ibrahim**Date:**2014**Type:**Text , Journal article**Relation:**European Journal of Operational Research Vol. 237, no. 3 (2014), p. 857-870**Full Text:**false**Reviewed:****Description:**With modern data-Acquisition equipment and on-line computers used during production, it is now common to monitor several correlated quality characteristics simultaneously in multivariate processes. Multivariate control charts (MCC) are important tools for monitoring multivariate processes. One difficulty encountered with multivariate control charts is the identification of the variable or group of variables that cause an out-of-control signal. Expert knowledge either in combination with wrapper-based supervised classifier or a pre-filter with wrapper are the standard approaches to detect the sources of out-of-control signal. However gathering expert knowledge in source identification is costly and may introduce human error. Individual univariate control charts (UCC) and decomposition of T2 statistics are also used in many cases simultaneously to identify the sources, but these either ignore the correlations between the sources or may take more time with the increase of dimensions. The aim of this paper is to develop a source identification approach that does not need any expert-knowledge and can detect out-of-control signal in less computational complexity. We propose, a hybrid wrapper-filter based source identification approach that hybridizes a Mutual Information (MI) based Maximum Relevance (MR) filter ranking heuristic with an Artificial Neural Network (ANN) based wrapper. The Artificial Neural Network Input Gain Measurement Approximation (ANNIGMA) has been combined with MR (MR-ANNIGMA) to utilize the knowledge about the intrinsic pattern of the quality characteristics computed by the filter for directing the wrapper search process. To compute optimal ANNIGMA score, we also propose a Global MR-ANNIGMA using non-functional relationship between variables which is independent of the derivative of the objective function and has a potential to overcome the local optimization problem of ANN training. The novelty of the proposed approaches is that they combine the advantages of both filter and wrapper approaches and do not require any expert knowledge about the sources of the out-of-control signals. Heuristic score based subset generation process also reduces the search space into polynomial growth which in turns reduces computational time. The proposed approaches were tested by exhaustive experiments using both simulated and real manufacturing data and compared to existing methods including independent filter, wrapper and Multivariate EWMA (MEWMA) methods. The results indicate that the proposed approaches can identify the sources of out-of-control signals more accurately than existing approaches. © 2014 Elsevier B.V. All rights reserved.

Methods for global optimization of nonsmooth functions with applications

**Authors:**Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Applied and Computational Mathematics Vol. 5, no. 1 (2006), p. 3-15**Full Text:**false**Reviewed:****Description:**In this survey paper we present some results obtained in the Centre for Informatics and Applied Optimization (CIAO) at University of Ballarat, Australia, in the area of numerical global optimization. We describe a conceptual scheme of two methods developed in CIAO and present results of numerical experiments with some real world problems. The paper is based on a plenary lecture given by the author at the First International Conference on Control and Optimization with Industrial Applications, Baku, Azerbaijan, 2005.**Description:**C1**Description:**2003001547

Optimisation solvers and problem formulations for solving a data clustering problem

**Authors:**Ugon, Julien , Rubinov, Alex**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005**Full Text:****Reviewed:****Description:**A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.**Description:**E1**Description:**2003001437

**Authors:**Ugon, Julien , Rubinov, Alex**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005**Full Text:****Reviewed:****Description:**A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.**Description:**E1**Description:**2003001437

Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in Rn

- Morales-Silva, Daniel, Gao, David

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2013**Type:**Text , Journal article**Relation:**Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282**Full Text:****Reviewed:****Description:**The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double- min duality is solved for a nonconvex optimization problem with double-well potential in ℝn, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2013**Type:**Text , Journal article**Relation:**Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282**Full Text:****Reviewed:****Description:**The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double- min duality is solved for a nonconvex optimization problem with double-well potential in ℝn, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

Literature on image segmentation based on split - and - Merge techniques

- Faruquzzaman, A. B. M., Paiker, Nafize, Arafat, Jahidul, Ali, Mortuza, Sorwar, Golam

**Authors:**Faruquzzaman, A. B. M. , Paiker, Nafize , Arafat, Jahidul , Ali, Mortuza , Sorwar, Golam**Date:**2008**Type:**Text , Conference proceedings , Conference paper**Relation:**ICITA 2008, Cairns, Qld., 23-26 June, ICITA, published in Proceedings of 5th International Conference on Information Technology and Application pp. 120-125.**Full Text:**false**Reviewed:****Description:**Image segmentation is a feverish issue due to drastically increasing the use of computer and the Internet. Various algorithms have been invented on this aspect. Among them, split-and-merge (SM) algorithm is highly lucrative now-a-days due to its simplicity and effectiveness in the sector of image processing. Numerous researchers have performed their research work on this algorithm to triumph over its drawbacks for its sustainable and competent implementation. This paper has consolidated the useful consideration and proposal of various researchers to formulate a strong base of knowledge for the future researcher. It has also tinted few unsettled drawbacks of SM algorithm which will open the casement of brainstorming as well as persuade them for future research on SM algorithm, thereby allow SM algorithm to attain a globally optimal algorithm for image segmentation.**Description:**5th International Conference on Information Technology and Applications, ICITA 2008

A global optimization approach to classification

- Bagirov, Adil, Rubinov, Alex, Yearwood, John

**Authors:**Bagirov, Adil , Rubinov, Alex , Yearwood, John**Date:**2002**Type:**Text , Journal article**Relation:**Optimization and Engineering Vol. 9, no. 7 (2002), p. 129-155**Full Text:**false**Reviewed:****Description:**In this paper is presented an hybrid algorithm for finding the absolute extreme point of a multimodal scalar function of many variables. The algorithm is suitable when the objective function is expensive to compute, the computation can be affected by noise and/or partial derivatives cannot be calculated. The method used is a genetic modification of a previous algorithm based on the Prices method. All information about behavior of objective function collected on previous iterates are used to chose new evaluation points. The genetic part of the algorithm is very effective to escape from local attractors of the algorithm and assures convergence in probability to the global optimum. The proposed algorithm has been tested on a large set of multimodal test problems outperforming both the modified Prices algorithm and classical genetic approach.**Description:**C1**Description:**2003000061

Are you sure you would like to clear your session, including search history and login status?