Optimality conditions in nonconvex optimization via weak subdifferentials
- 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.
A filled function method for nonlinear equations
- Authors: Wu, Zhiyou , Mammadov, Musa , Bai, Fusheng , Yang, Y. J.
- Date: 2007
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 189, no. 2 (2007), p. 1196-1204
- Full Text: false
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- Description: In this paper, we propose a new global optimization approach based on the filled function method for solving box-constrained systems of nonlinear equations. The special properties of optimization problem are employed to construct a novel filled function. The objective function value can be reduced by half in each iteration of our filled function algorithm. Several numerical examples are presented to illustrate the efficiency of the present approach.
- Description: C1
- Description: 2003005618
Multi label classification and drug-reaction associations using global optimization techniques
- Authors: Mammadov, Musa , Yearwood, John , Aliyea, Leyla
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
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- Description: E1
- Description: 2003000890
Statistical convergence and turnpike theory
- Authors: Mammadov, Musa
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 3713-3718
- Full Text: false
- Description: This article considers the application of the notion of statistical convergence in turnpike theory. The first results have been obtained recently [, , ]. We briefly discuss the importance of this conjunction, present some results obtained and, finally, we formulate a challenge problem for future investigations.
- Description: 2003007533
A new filled function method for nonlinear equations
- Authors: Lin, Yongjian Jian , Yang, Y. , Mammadov, Musa
- Date: 2009
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. , no. (2009), p.
- Full Text: false
- Description: In this paper, a new global optimization approach based on the filled function method is proposed for solving box-constrained systems of nonlinear equations. We first convert the nonlinear system into an equivalent global optimization problem, and then propose a new filled function method to solve the converted global optimization problem. Several numerical examples are presented and solved by using different local minimization methods, which illustrate the efficiency of the present approach. © 2009 Elsevier Inc. All rights reserved.
Turnpike theory : Stability of optimal trajectories
- Authors: Mammadov, Musa
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 3948-3955
- Full Text: false
Dynamical systems based on a fuzzy derivative and its applications to data classification
- Authors: Mammadov, Musa , Rubinov, Alex , Yearwood, John
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the Industrial Optimisation 2003 Conference, Perth : 30th September, 2002
- Full Text: false
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- Description: E1
- Description: 2003000339
An optimization approach to the study of drug-drug interactions
- 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
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- 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
A comparison of two methods to establish drug-reaction relationships in the ADRAC database
- Authors: Mammadov, Musa , Saunders, Gary
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at the Fourth International ICSC Symposium on Engineering of Intelligent Systems (EIS 2004), Island of Madeira, Portugal, Island of Madeira, Portugal : 29th February, 2004
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- Description: Adverse drug reactions (ADRs) are estimated to be one of the leading causes of death. Many national and international agencies have set up databases of ADR reports for the express purpose of determining the relationship between drugs and adverse reactions that they cause. We formulate the drug-reaction relationship problem as a continuous optimization problem and utilize C-GRASP, a new continuous global optimization heuristic, to approximately determine the relationship between drugs and adverse reactions. Our approach is compared against others in the literature and is shown to find better solutions. 1.
- Description: E1
- Description: 2003000897
A filled function method for box-constrained system of nonlinear equations
- Authors: Wu, Zhiyou , Mammadov, Musa , Bai, Fusheng
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at APCCAS 2006. IEEE Asia Pacific Conference on Circuits and Systems, Singapore : 4th -7th Dececmber, 2006 p. 623-626
- Full Text: false
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- Description: In this paper, we present a global optimization method based on the filled function method to solve systems of nonlinear equations. Formulating a system of nonlinear equation into an equivalent global optimization problem, we manage to find a solution or an appropriate solution of the system of nonlinear equations by solving the formulated global optimization problem. A novel filled function method is proposed to solve the global optimization problem. Two numerical examples are presented to illustrate the efficiency of this method.
- Description: E1
- Description: 2003001840
A new global optimization algorithm based on a dynamical systems approach
- Authors: Mammadov, Musa
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
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- Description: The purpose of the paper is to develop and study new techniques for global optimization based on dynamical systems approach. This approach uses the notion of relationship between variables which describes influences of the changes of the variables to each other. A numerical algorithm for global optimization is introduced.
- Description: E1
- Description: 2003000892
Solving a system of nonlinear integral equations by an RBF network
- Authors: Golbabai, A. , Mammadov, Musa , Seifollahi, Sattar
- Date: 2009
- Type: Text , Journal article
- Relation: Computers & Mathematics with Applications Vol. 57, no. 10 (2009), p. 1651-1658
- Full Text: false
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- Description: In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to Update the weights of RBFN is Studied in solving systems of nonlinear integral equations. (C) 2009 Elsevier Ltd. All rights reserved.
Quantification of intermarket influence based on the global optimization and its application for stock market prediction
- Authors: Tilakaratne, Chandima , Mammadov, Musa , Hurst, Cameron
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at Integrating AI and Data Mining, 1st International Workshop Proceedings, Hobart, Tasmania : 4th - 5th December, 2006
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- Description: This study investigates how intermarket influences can be used to help the prediction of the direction (up or down) of the next day's close price of the Australian All Ordinary Index (AORD). First, intermarket influences from the potential influential markets on the AORD are quantified by assigning weights for all influential markets. The weights were defined as a solution to an optimization problem which aims to maximise rank correlation between the current day's relative return of the AORD and the weighted sum of lagged relative returns of the potential influential markets. Then, the next day's relative return of the AORD is predicted by applying the neural networks as a classifier. Two different scenarios were compared: 1) using the current day's relative returns of different sets of influential markets as separate inputs; and, 2) using only the weighted sum of these relative returns as a "combined market". The results revealed that the second approach provides better predictions in all cases. This shows the effectiveness of the proposed approach for quantifying intermarket influences and the potential of using the "weighted combined markets" for the prediction
- Description: E1
- Description: 2003001609
A hybrid clustering algorithm using two level of abstraction
- Authors: Ghosh, Ranadhir , Mammadov, Musa , Ghosh, Moumita , Yearwood, John
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at Fuzzy Logic, Soft Computing, and Computational Intelligence, 11th International Fuzzy Systems Association World Congress, Beijing, China : 28th - 31st July, 2005
- Full Text: false
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- Description: E1
- Description: 2003001360
Classification on shorter featured and multi-label datasets
- Authors: Mammadov, Musa
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 7th International Conference on Optimization: Techniques and Applications, ICOTA7, Kobe International Conference Center, Japan : 12th-15th December 2007
- Full Text: false
- Description: 2003005711
Statistical cluster points of sequences in finite dimensional spaces
- Authors: Pehlivan, Serpil , Guncan, A. , Mammadov, Musa
- Date: 2004
- Type: Text , Journal article
- Relation: Czechoslovak Mathematical Journal Vol. 54, no. 1 (2004), p. 95-102
- Full Text: false
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- Description: In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of T-statistical convergence. A sequence x is
- Description: C1
- Description: 2003000896
Statistical limit inferior and limit superior for sequences of fuzzy numbers
- Authors: Aytar, Salih , Mammadov, Musa , Pehlivan, Serpil
- Date: 2006
- Type: Text , Journal article
- Relation: Fuzzy Sets and Systems Vol. 157, no. 7 (2006), p. 976-985
- Full Text: false
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- Description: In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers. © 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001832
A study of drug-reaction relationships in Australian drug safety data
- Authors: Mammadov, Musa , Saunders, Gary , Dekker, Evan
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the 2nd Australian Data Mining Workshop, Sydney, New South Wales : 8th December, 2003
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- Description: The sparse nature of voluntarily reported drug safety data benefits from a system that consolidates the massive amount of data into a manageable format for analysis. This has been done for Australian drug safety data by the Australian Adverse Drug Reaction Advisory Committee (ADRAC) for reactions using the systems organ class (SOC) ontology. There has long been a need for a similar kind of grouping to apply to drugs in this type of data. In ADRAC, drugs are currently listed by trade-name, where only some of these trade-names were assigned anatomical-therapeutic-chemical classification (ATC) codes. We assigned an ATC code for each ADRAC trade-name and show that this ontology facilitates the detection of drug class / reaction class associations at various levels of specificity. This allows different views of these associations (even very rare ones) and their significance measured for the development of more sensitive signal detection methods. We report that this ATC classification enables both the grouping of association rule approach that is useful for studying rare associations, and the development of an adverse reaction signal detection method.
- Description: E1
- Description: 2003000340
An auxiliary function method for constrained systems of nonlinear equations
- Authors: Wu, Zhiyou , Bai, Fusheng , Mammadov, Musa
- Date: 2008
- Type: Text , Conference paper
- Relation: Paper presented at 20th EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT-2008, Neringa, Lithuania : 20th-23rd May 2008 p. 259-265
- Full Text: false
- Description: In this paper, we propose an auxiliary function method to solve constrained systems of nonlinear equations. By introducing an auxiliary function, an unconstrained (box-constrained) optimization problem is constructed for a given constrained system of nonlinear equations. It is shown that any local minimizer of the constructed unconstrained optimization problem is an approximate solution to the given constrained system when parameters are appropriately chosen, and the precision for approximation can be preset. It is also shown that any accumulation point of the local minimizers of the constructed unconstrained optimization problems with a sequence of parameters tending to zero is a solution to the given constrained system of nonlinear equations.
A fuzzy derivative approach to classification of outcomes from the ADRAC database
- Authors: Mammadov, Musa , Saunders, Gary , Yearwood, John
- Date: 2004
- Type: Text , Journal article
- Relation: International Transactions in Operational Research Vol. 11, no. 2 (2004), p. 169-180
- Full Text: false
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- Description: The Australian Adverse Drug Reaction Advisory Committee (ADRAC) database has been collected and maintained by the Therapeutic Goods Administration. In this paper we study a part of his database (Card2) which contains records having just reactions from the Cardiovascular group. Drug-reaction relationships are presented by a vector of degrees which shows the degree of association of a drug with each class of reactions. In this work we examine these relationships in the classification of reaction outcomes. A modified version of the fuzzy derivative method (FDM2) is used for classification.
- Description: C1
- Description: 2003000895