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Vibration analysis : Optimization of parameters of the two mass model based on Kelvin elements

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

A formula for multiple classifiers in data mining based on Brandt semigroups

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

  • Authors: Kelarev, Andrei , Yearwood, John , Mammadov, Musa
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Semigroup Forum Vol. 78, no. 2 (2009), p. 293-309
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  • Description: A general approach to designing multiple classifiers represents them as a combination of several binary classifiers in order to enable correction of classification errors and increase reliability. This method is explained, for example, in Witten and Frank (Data Mining: Practical Machine Learning Tools and Techniques, 2005, Sect. 7.5). The aim of this paper is to investigate representations of this sort based on Brandt semigroups. We give a formula for the maximum number of errors of binary classifiers, which can be corrected by a multiple classifier of this type. Examples show that our formula does not carry over to larger classes of semigroups. © 2008 Springer Science+Business Media, LLC.

A new filled function method for nonlinear equations

- Lin, Yongjian Jian, Yang, Y., Mammadov, Musa

  • Authors: Lin, Yongjian Jian , Yang, Y. , Mammadov, Musa
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Applied Mathematics and Computation Vol. , no. (2009), p.
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  • 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.

Asymptotical stability of optimal paths in nonconvex problems

- Mammadov, Musa

  • Authors: Mammadov, Musa
  • Date: 2009
  • Type: Text , Book chapter
  • Relation: Optimization Chapter 5 p. 95-134
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  • Description: In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion . We study the infinite horizon problem of maximizing the functional as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.
  • Description: 2003007899

Modified neural network algorithms for predicting trading signals of stock market indices

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

  • Authors: Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Journal of Applied Mathematics and Decision Sciences Vol. 2009, no. (2009), p.
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  • Description: The aim of this paper is to present modified neural network algorithms to predict whether it is best to buy, hold, or sell shares (trading signals) of stock market indices. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The modified network algorithms are based on the structure of feed forward neural networks and a modified Ordinary Least Squares (OLSs) error function. An adjustment relating to the contribution from the historical data used for training the networks and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. These algorithms were employed to predict the trading signals of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions.

On weak subdifferentials, directional derivatives, and radial epiderivatives for nonconvex functions

- Kasimbeyli, Refail, Mammadov, Musa

  • Authors: Kasimbeyli, Refail , Mammadov, Musa
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Siam Journal on Optimization Vol. 20, no. 2 (2009), p. 841-855
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  • Description: In this paper we study relations between the directional derivatives, the weak subdifferentials, and the radial epiderivatives for nonconvex real-valued functions. We generalize the well-known theorem that represents the directional derivative of a convex function as a pointwise maximum of its subgradients for the nonconvex case. Using the notion of the weak subgradient, we establish conditions that guarantee equality of the directional derivative to the pointwise supremum of weak subgradients of a nonconvex real-valued function. A similar representation is also established for the radial epiderivative of a nonconvex function. Finally the equality between the directional derivatives and the radial epiderivatives for a nonconvex function is proved. An analogue of the well-known theorem on necessary and sufficient conditions for optimality is drawn without any convexity assumptions.

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

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

Optimization of parameters of the Kelvin element in vibration analysis

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

Solving a system of nonlinear integral equations by an RBF network

- Golbabai, A., Mammadov, Musa, Seifollahi, Sattar

  • 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
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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.

Statistical convergence and turnpike theory

- Mammadov, Musa

  • Authors: Mammadov, Musa
  • Date: 2009
  • Type: Text , Book chapter
  • Relation: Encyclopedia of Optimization Chapter p. 3713-3718
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  • 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

Turnpike theory : Stability of optimal trajectories

- Mammadov, Musa

A filled function method for constrained nonlinear equations

- Bai, Fusheng, Mammadov, Musa, Wu, Zhiyou, Yang, Yongjian

  • Authors: Bai, Fusheng , Mammadov, Musa , Wu, Zhiyou , Yang, Yongjian
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Pacific Journal of Optimization Vol. 4, no. 1 (Jan 2008), p. 9-18
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  • Description: We consider the problem of solving a constrained system of nonlinear equations. After reformulating the system into an equivalent constrained global optimization problems, we construct a filled function based on a special property of the reformulated problem. A filled function method is then proposed to solve the constrained system of nonlinear equations. Some numerical examples are presented to illustrate the usefulness of the present techniques.
  • Description: C1

An auxiliary function method for constrained systems of nonlinear equations

- Wu, Zhiyou, Bai, Fusheng, Mammadov, Musa

  • 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
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  • 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.

An inexact modified subgradient algorithm for nonconvex optimization

- Burachik, Regina, Kaya, Yalcin, Mammadov, Musa

  • Authors: Burachik, Regina , Kaya, Yalcin , Mammadov, Musa
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Computational Optimization and Applications Vol. , no. (2008), p. 1-24
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  • Description: We propose and analyze an inexact version of the modified subgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may allow to solve problems with less computational effort. We illustrate this through test problems, including an optimal bang-bang control problem, under several different inexactness schemes. © 2008 Springer Science+Business Media, LLC.
  • Description: C1

An optimization approach to identify the relationship between features and output of a multi-label classifier

- Mammadov, Musa

Predicting trading signals of stock market indices using neural networks

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

  • Authors: Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney
  • Date: 2008
  • Type: Text , Conference paper
  • Relation: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Auckland 1 December 2008 through 5 December 2008 Vol. 5360 LNAI, p. 522-531
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  • Description: The aim of this paper is to develop new neural network algorithms to predict trading signals: buy, hold and sell, of stock market indices. Most commonly used classification techniques are not suitable to predict trading signals when the distribution of the actual trading signals, among theses three classes, is imbalanced. In this paper, new algorithms were developed based on the structure of feedforward neural networks and a modified Ordinary Least Squares (OLS) error function. An adjustment relating to the contribution from the historical data used for training the networks, and the penalization of incorrectly classified trading signals were accounted for when modifying the OLS function. A global optimization algorithm was employed to train these networks. The algorithms developed in this study were employed to predict the trading signals of day (t+1) of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions. © 2008 Springer Berlin Heidelberg.

Predicting trading signals of the All Share Price Index Using a modified neural network algorithm

- Tilakaratne, Chandima, Tissera, J.H.D.S.P, Mammadov, Musa

  • Authors: Tilakaratne, Chandima , Tissera, J.H.D.S.P , Mammadov, Musa
  • Date: 2008
  • Type: Text , Conference paper
  • Relation: Proceedings of the 9th International Information Technology Conference; 28th-29th October, 2008, Colombo , Sri Lanka
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  • Description: This study predicts whether it is best to buy, hold or sell shares (trading signals) of the All Share Price Index (ASPI) of the Colombo Stock Exchange, using a modified neural network (NN) algorithm. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The structure of this modified neural network is same as that of feedforward neural networks. This algorithm minimises a modified Ordinary Least Squares (OLS) error function. An adjustment relating to the contribution from the historical data used for training the networks, and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. Results obtained were satisfactory.

The core of a sequence of fuzzy numbers

- Aytar, Salih, Pehlivan, Serpil, Mammadov, Musa

  • Authors: Aytar, Salih , Pehlivan, Serpil , Mammadov, Musa
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Fuzzy Sets and Systems Vol. 159, no. 24 (2008), p. 3369-3379
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  • Description: In this paper, based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties. We extend the concept of the core of a sequence of complex numbers, first introduced by Knopp in 1930, to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval [ν, μ] where ν and μ are extreme limit points of the sequence. © 2008 Elsevier B.V. All rights reserved.

To be fair or efficient or a bit of both

- Zukerman, Moshe, Mammadov, Musa, Tan, Liansheng, Ouveysi, Iradj, Andrew, Lachlan

  • Authors: Zukerman, Moshe , Mammadov, Musa , Tan, Liansheng , Ouveysi, Iradj , Andrew, Lachlan
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Computers and Operations Research Vol. 35, no. 12 (2008), p. 3787-3806
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  • Description: IIntroducing a new concept of (®, ¯)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 · ® · 1, nor more than ¯ ¸ 1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (®, ¯)-fairness constraints. This leads to what we call an efficiency-fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of example from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.
  • Description: C1

A filled function method for nonlinear equations

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

  • 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
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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