Turnpike theorem for an infinite horizon optimal control problem with time delay
- Authors: Mammadov, Musa
- Date: 2014
- Type: Text , Journal article
- Relation: SIAM Journal on Control and Optimization Vol. 52, no. 1 (2014), p. 420-438
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- Description: An optimal control problem for systems described by a special class of nonlinear differential equations with time delay is considered. The cost functional adopted could be considered as an analogue of the terminal functional defined over an infinite time horizon. The existence of optimal solutions as well as the asymptotic stability of optimal trajectories (that is, the turnpike property) are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem. Such mild restrictions on the nonlinearities allowed us to apply these results to a blood cell production model. © 2014 Society for Industrial and Applied Mathematics.
Using meta-regression data mining to improve predictions of performance based on heart rate dynamics for Australian football
- Authors: Jelinek, Herbert , Kelarev, Andrei , Robinson, Dean , Stranieri, Andrew , Cornforth, David
- Date: 2014
- Type: Text , Journal article
- Relation: Applied Soft Computing Vol. 14, no. PART A (2014), p. 81-87
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- Description: This work investigates the effectiveness of using computer-based machine learning regression algorithms and meta-regression methods to predict performance data for Australian football players based on parameters collected during daily physiological tests. Three experiments are described. The first uses all available data with a variety of regression techniques. The second uses a subset of features selected from the available data using the Random Forest method. The third used meta-regression with the selected feature subset. Our experiments demonstrate that feature selection and meta-regression methods improve the accuracy of predictions for match performance of Australian football players based on daily data of medical tests, compared to regression methods alone. Meta-regression methods and feature selection were able to obtain performance prediction outcomes with significant correlation coefficients. The best results were obtained by the additive regression based on isotonic regression for a set of most influential features selected by Random Forest. This model was able to predict athlete performance data with a correlation coefficient of 0.86 (p < 0.05). © 2013 Published by Elsevier B.V. All rights reserved.
- Description: C1
A new auxiliary function method for general constrained global optimization
- Authors: Wu, Zhiyou , Bai, Fusheng , Yang, Yongjian , Mammadov, Musa
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Vol. 62, no. 2 (2013), p. 193-210
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- Description: In this article, we first propose a method to obtain an approximate feasible point for general constrained global optimization problems (with both inequality and equality constraints). Then we propose an auxiliary function method to obtain a global minimizer or an approximate global minimizer with a required precision for general global optimization problems by locally solving some unconstrained programming problems. Some numerical examples are reported to demonstrate the efficiency of the present optimization method. © 2013 Taylor & Francis.
- Description: 2003011103
An algorithm for minimization of pumping costs in water distribution systems using a novel approach to pump scheduling
- Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
- Date: 2013
- Type: Text , Journal article
- Relation: Mathematical and Computer Modelling Vol. 57, no. 3-4 (2013), p. 873-886
- Relation: http://purl.org/au-research/grants/arc/LP0990908
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- Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. This is different from other approaches where binary integer variables for each hour are typically used, which is considered very impractical from an operational perspective. The problem is formulated as a mixed integer nonlinear programming problem, and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet. © 2012 Elsevier Ltd.
- Description: 2003010583
Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in Rn
- 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
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- 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.
Euler-Goursat-like formula via Laplace-Borel duality
- Authors: Gurarii, V. P. , Gillam, David
- Date: 2013
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 408, no. 2 (2013), p. 655-668
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- Description: The Goursat formula for the hypergeometric function extends the Euler-Gauss relation to the case of logarithmic singularities. We study the monodromic functional equation associated with a perturbation of the Bessel differential equation by means of a variant of the Laplace-Borel technique: we introduce and study a related monodromic equation in the dual complex plane. This construction is a crucial element in our proof of a duality theorem that leads to an extension of the Euler-Gauss-Goursat formula for hypergeometric functions to a substantially larger class of functions. © 2013 Elsevier Ltd.
- Description: C1
Extraction and processing of real time strain of embedded FBG sensors using a fixed filter FBG circuit and an artificial neural network
- Authors: Kahandawa, Gayan , Epaarachchi, Jayantha , Wang, Hao , Canning, John , Lau, Alan
- Date: 2013
- Type: Text , Journal article
- Relation: Measurement: Journal of the International Measurement Confederation Vol. 46, no. 10 (2013), p. 4045-4051
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- Description: Fibre Bragg Grating (FBG) sensors have been used in the development of structural health monitoring (SHM) and damage detection systems for advanced composite structures over several decades. Unfortunately, to date only a handful of appropriate configurations and algorithm sare available for using in SHM systems have been developed. This paper reveals a novel configuration of FBG sensors to acquire strain reading and an integrated statistical approach to analyse data in real time. The proposed configuration has proven its capability to overcome practical constraints and the engineering challenges associated with FBG-based SHM systems. A fixed filter decoding system and an integrated artificial neural network algorithm for extracting strain from embedded FBG sensor were proposed and experimentally proved. Furthermore, the laboratory level experimental data was used to verify the accuracy of the system and it was found that the error levels were less than 0.3% in predictions. The developed SMH system using this technology has been submitted to US patent office and will be available for use of aerospace applications in due course. © 2013 Elsevier Ltd. All rights reserved.
Finite element computations over quadtree meshes : Strain smoothing and semi-analytical formulation
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2013
- Type: Text , Journal article
- Relation: International Journal of Advances in Engineering Sciences and Applied Mathematics Vol. 7, no. 3 (2013), p. 124-133
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- Description: In this paper, we discuss two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta (Int J Numer Methods Eng 12:35, 1978) or Tabarraei and Sukumar (Finite Elem Anal Des 41:686, 2005). Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.
Fractal bodies invisible in 2 and 3 directions
- Authors: Plakhov, Alexander , Roshchina, Vera
- Date: 2013
- Type: Text , Journal article
- Relation: Discrete and Continuous Dynamical Systems - Series A Vol. 33, no. 4 (2013), p. 1615-1631
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- Description: We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and threedimensional bodies invisible in one and two orthogonal directions were constructed.
- Description: 2003010679
Globally convergent algorithms for solving unconstrained optimization problems
- Authors: Taheri, Sona , Mammadov, Musa , Seifollahi, Sattar
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Vol. , no. (2013), p. 1-15
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- Description: New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also, the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.
Hyperbolic smoothing function method for minimax problems
- Authors: Bagirov, Adil , Al Nuaimat, Alia , Sultanova, Nargiz
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Vol. 62, no. 6 (2013), p. 759-782
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- Description: In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem. © 2013 Copyright Taylor and Francis Group, LLC.
- Description: 2003011099
On large bipartite graphs of diameter 3
- Authors: Feria-Purón, Ramiro , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2013
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 313, no. 4 (2013), p. 381-390
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: We consider the bipartite version of the degree/diameter problem, namely, given natural numbers d≥2 and D≥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d and diameter D. In this context, the bipartite Moore bound Mb(d,D) represents a general upper bound for Nb(d,D). Bipartite graphs of order Mb(d,D) are very rare, and determining Nb(d,D) still remains an open problem for most (d,D) pairs. This paper is a follow-up of our earlier paper (Feria-Purón and Pineda-Villavicencio, 2012 [5]), where a study on bipartite (d,D,-4)-graphs (that is, bipartite graphs of order M b(d,D)-4) was carried out. Here we first present some structural properties of bipartite (d,3,-4)-graphs, and later prove that there are no bipartite (7,3,-4)-graphs. This result implies that the known bipartite (7,3,-6)-graph is optimal, and therefore Nb(7,3)=80. We dub this graph the Hafner-Loz graph after its first discoverers Paul Hafner and Eyal Loz. The approach here presented also provides a proof of the uniqueness of the known bipartite (5,3,-4)-graph, and the non-existence of bipartite (6,3,-4)-graphs. In addition, we discover at least one new largest known bipartite-and also vertex-transitive-graph of degree 11, diameter 3 and order 190, a result which improves by four vertices the previous lower bound for Nb(11,3). © 2012 Elsevier B.V. All rights reserved.
- Description: 2003011037
Preface: Special issue of JOGO MEC EurOPT 2010-Izmir
- Authors: Kasimbeyli, Refail , Mammadov, Musa , Dincer, Cemali
- Date: 2013
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 56, no. 2 (June 2013), p. 217-218
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- Description: C1
Reachability and controllability of linear switched impulsive systems
- Authors: Liu, Chao , Han, Qi , Li, Chuandong , Zhang, Qun
- Date: 2013
- Type: Text , Journal article
- Relation: IET Control Theory and Applications Vol. 7, no. 9 (2013), p. 1294-1299
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- Description: This study investigates the reachability and controllability of linear switched impulsive systems in which impulsive component is independent of switching among different subsystems. Some crucial geometrical criteria are established. The authors present the fact that the reachable sets and the controllable sets may not be subspaces, if impulsive matrices are singular. While impulsive matrices are reversible, the reachable and controllable subspaces can be determined by two proposed subspace algorithms. The authors also point out that the reachable or controllable subspace is an invariant subspace of the considered systems. Finally, two simple corresponding examples are discussed to illustrate the correctness and effectiveness of the proposed theoretical results. © The Institution of Engineering and Technology 2013.
- Description: C1
Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm
- Authors: Gao, David , Watson, Layne , Easterling, David , Thacker, William , Billups, Stephen
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 28, no. 2 (2013), p. 313-326
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- Description: This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for solving nonconvex quadratic minimization problems with either box or1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems (with zero duality gap). Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported. © 2013 Copyright Taylor and Francis Group, LLC.
- Description: 2003010580
Synchronization properties of trees in the kuramoto model
- Authors: Dekker, Anthony , Taylor, Richard
- Date: 2013
- Type: Text , Journal article
- Relation: SIAM Journal on Applied Dynamical Systems Vol. 12, no. 2 (2013), p. 596-617
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- Description: We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For several classes of tree, and for both uniform and Gaussian vertex frequency distributions, we provide tight closed-form bounds and empirical expressions for the expected value of the critical coupling. We also provide several bounds on the expected value of the critical coupling for all trees. Finally, we show that for a given set of vertex frequencies, there is a rearrangement of oscillator frequencies for which the critical coupling is bounded by the spread of frequencies. © 2013 Society for Industrial and Applied Mathematics.
- Description: C1
A complementarity partition theorem for multifold conic systems
- Authors: Peña, Javier , Roshchina, Vera
- Date: 2012
- Type: Text , Journal article
- Relation: Mathematical Programming Vol.142 , no.1-2 (2012), p.579-589
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- Description: Consider a homogeneous multifold convex conic system {Mathematical expression}and its alternative system {Mathematical expression}, where K 1,..., K r are regular closed convex cones. We show that there is a canonical partition of the index set {1,..., r} determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming. © 2012 Springer and Mathematical Optimization Society.
A new method for solving linear ill-posed problems
- Authors: Zhang, Jianjun , Mammadov, Musa
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 20 (2012), p.10180-10187
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- Description: In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush-Kuhn-Tucker conditions, Fisher-Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the proposed method is effective and promising for many practical problems. © 2012.
An extended lifetime measure for telecommunications networks : Improvements and implementations
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Bektas, Tolga
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 3 (2012), p. 639-649
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- Description: Predicting the lifetime of a network is a stochastic and very hard task. Sensitivity analysis of a network in order to identify the weakest points in the network, provides valuable knowledge to draw an optimum investment strategy for the expansion of the networks for the network carriers. To achieve this goal, a new measure, called topology lifetime, was recently proposed for measuring the performance of a telecommunication network. This measure not only allows to perform a sensitivity analysis of the networks, but also it provides the means to compare the different topologies with respect to the ability of the network in supporting growth in network traffic before new capacity/facility is installed. This paper addresses some improvements upon the previously defined measures and presents the implementation results of the various lifetime measure methodologies. Computational analysis on some commonly used topologies show how the new measure can be utilized in assessing network performance.
- Description: 2003010401
Anticipating synchronization through optimal feedback control
- Authors: Huang, Tingwen , Gao, David , Li, Chuandong , Xiao, MingQing
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 52, no. 2 (2012), p. 281-290
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- Description: In this paper, we investigate the anticipating synchronization of a class of coupled chaotic systems through discontinuous feedback control. The stability criteria for the involved error dynamical system are obtained by means of model transformation incorporated with Lyapunov functional and linear matrix inequality. Also, we discuss the optimal designed controller based on the obtained criteria. The numerical simulation is presented to demonstrate the theoretical results. © 2011 Springer Science+Business Media, LLC.