List of Titles

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A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case

- Kasimbeyli, Nergiz, Kasimbeyli, Refail, Mammadov, Musa

Authors: Kasimbeyli, Nergiz , Kasimbeyli, Refail , Mammadov, Musa
Date: 2016
Type: Text , Journal article
Relation: Optimization Vol. 65, no. 5 (May 2016), p. 937-945
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Description: The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.

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. Â© 2011 Elsevier Ltd. All rights reserved.

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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.

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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.

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Coverage in WLAN : Optimization model and algorithm

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

Authors: Kouhbor, Shahnaz , Ugon, Julien , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
Date: 2006
Type: Text , Conference paper
Relation: Paper presented at the First International Conference on Wireless Broadband and Ultra Wideband Communications, AusWireless 2006, Sydney : 13th March, 2006
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Description: When designing wireless communication systems, it is very important to know the optimum numbers of access points (APs) in order to provide a reliable design. In this paper we describe a mathematical model developed for finding the optimal number and location of APs. A new Global Optimization Algorithm (AGOP) is used to solve the problem. Results obtained demonstrate that the model and software are able to solve optimal coverage problems for design areas with different types of obstacles and number of users.
Description: 2003001757

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Coverage in WLAN with minimum number of access points

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

Authors: Kouhbor, Shahnaz , Ugon, Julien , Rubinov, Alex , Kruger, Alexander , Mammadov, Musa
Date: 2006
Type: Text , Conference paper
Relation: Paper presented at VTC 2006 - Spring, 2006 IEEE 63rd Vehicular Technology Conference, Melbourne : 7th May, 2006
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Description: E1
Description: 2003001610

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Optimization of parameters of the Kelvin element in vibration analysis

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

Authors: Kuznetsov, Alexey , Mammadov, Musa , Hajilarov, Eldar
Date: 2009
Type: Text , Conference paper
Relation: Paper presented at 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC January 2009
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Description: In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.

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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

Authors: Kuznetsov, Alexey , Mammadov, Musa , Sultan, Ibrahim , Hajilarov, Eldar
Date: 2010
Type: Text , Conference paper
Relation: Paper presented at 8th IEEE International Conference on Control and Automation, ICCA 2010, Asia Gulf Hotel, Xiamen, China : 9th-11th June 2010 p. 1326-1332
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Description: In this paper we consider the problem of finding optimal parameters of the two mass model that represents vehicle suspension systems. The analysis of the problem is based on finding analytical solution of the system of coupled Ordinary Differential Equations (ODE). Such a technique allows us to generate optimization problem, where an objective function should be minimized, in accordance with ISO 2631 standard formula of admissible acceleration levels. That ensures maximum comfort for a driver and passenger in a moving vehicle on the considered highways.
Description: 2003008232

Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis

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

Authors: Kuznetsov, Alexey , Mammadov, Musa , Sultan, Ibrahim , Hajilarov, Eldar
Date: 2011
Type: Text , Journal article
Relation: Archive of Applied Mechanics Vol. 81, no. 10 (2011), p. 1427-1437
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Description: In this paper, we analyze an improved suspension system with the incorporated inerter device of the quarter-car model to obtain optimal design parameters for maximum comfort level for a driver and passengers. That is achieved by finding the analytical solution for the system of ordinary differential equations, which enables us to generate an optimization problem whose objective function is based on the international standards of admissible acceleration levels (ISO 2631-1, Mechanical Vibration and Shock-Evaluation of Human Exposure to Whole-Body Vibration-Part 1, 1997). The considered approach ensures the highest level of comfort for the driver and passengers due to a favorable reduction in body vibrations. Numerical examples, based on actually measured road profiles, are presented at the end of the paper to prove the validity of the proposed approach and its suitability for the problem at hand. Â© 2010 Springer-Verlag.

Optimization of a quarter-car suspension model coupled with the driver biomechanical effects

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

Authors: Kuznetsov, Alexey , Mammadov, Musa , Sultan, Ibrahim , Hajilarov, Eldar
Date: 2011
Type: Text , Journal article
Relation: Journal of Sound and Vibration Vol. 330, no. 12 (2011), p. 2937-2946
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Description: In this paper a Human–Vehicle–Road (HVR) model, comprising a quarter-car and a biomechanical representation of the driver, is employed for the analysis. Differential equations are provided to describe the motions of various masses under the inﬂuence of a harmonic road excitation. These equations are, subsequently, solved to obtain a closed form mathematical expression for the steady-state vertical acceleration measurable at the vehicle–human interface. The solution makes it possible to ﬁnd optimal parameters for the vehicle suspension system with respect to a speciﬁed ride comfort level. The quantitative deﬁnition given in the ISO 2631 standard for the ride comfort level is adopted in this paper for the optimization procedure. Numerical examples, based on actually measured road proﬁles, are presented to prove the validity of the proposed approach and its suitability for the problem at hand.

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.

Multi label classification and drug-reaction associations using global optimization techniques

- Mammadov, Musa, Yearwood, John, Aliyea, Leyla

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
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Description: E1
Description: 2003000890

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

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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
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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

- Mammadov, Musa, Saunders, Gary

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 new global optimization algorithm based on a dynamical systems approach

- Mammadov, Musa

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
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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

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