A BMI approach to guaranteed cost control of discrete-time uncertain system with both state and input delays
- Authors: Zhou, Xiaojun , Dong, Tianxue , Tang, Xiaolin , Yang, Chunhua , Gui, Weihua
- Date: 2015
- Type: Text , Journal article
- Relation: Optimal Control Applications and Methods Vol. 36, no. 6 (2015), p. 844-852
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- Description: In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi-definite optimization solver - PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.
A comparison of bidding strategies for online auctions using fuzzy reasoning and negotiation decision functions
- Authors: Kaur, Preetinder , Goyal, Madhu , Lu, Jie
- Date: 2017
- Type: Text , Journal article
- Relation: IEEE Transactions on Fuzzy Systems Vol. 25, no. 2 (2017), p. 425-438
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- Description: Bidders often feel challenged when looking for the best bidding strategies to excel in the competitive environment of multiple and simultaneous online auctions for same or similar items. Bidders face complicated issues for deciding which auction to participate in, whether to bid early or late, and how much to bid. In this paper, we present the design of bidding strategies, which aim to forecast the bid amounts for buyers at a particular moment in time based on their bidding behavior and their valuation of an auctioned item. The agent develops a comprehensive methodology for final price estimation, which designs bidding strategies to address buyers' different bidding behaviors using two approaches: Mamdani method with regression analysis and negotiation decision functions. The experimental results show that the agents who follow fuzzy reasoning with a regression approach outperform other existing agents in most settings in terms of their success rate and expected utility.
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 counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections
- Authors: Cominetti, Roberto , Roshchina, Vera , Williamson, Andrew
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Vol. 68, no. 1 (2019), p. 3-12
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- Description: The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the ε-under-relaxed cyclic projection method converge when ε ↓ 0 towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in R3 for which the ε-under-relaxed cycles do not converge. © 2018 Informa UK Limited, trading as Taylor & Francis Group.
A DC programming approach for sensor network localization with uncertainties in anchor positions
- Authors: Wu, Changzhi , Li, Chaojie , Long, Qiang
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 10, no. 3 (2014), p. 817-826
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- Description: The sensor network localization with uncertainties in anchor positions has been studied in this paper. We formulate this problem as a DC (difference of two convex functions) programming. Then, a DC programming based algorithm has been proposed to solve such a problem. Simulation results obtained by our proposed method are better performance than those obtained by existing ones.
A difference of convex optimization algorithm for piecewise linear regression
- Authors: Bagirov, Adil , Taheri, Sona , Asadi, Soodabeh
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 15, no. 2 (2019), p. 909-932
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
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- Description: The problem of finding a continuous piecewise linear function approximating a regression function is considered. This problem is formulated as a nonconvex nonsmooth optimization problem where the objective function is represented as a difference of convex (DC) functions. Subdifferentials of DC components are computed and an algorithm is designed based on these subdifferentials to find piecewise linear functions. The algorithm is tested using some synthetic and real world data sets and compared with other regression algorithms.
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
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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
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
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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
A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case
- 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.
A heuristic algorithm for solving the minimum sum-of-squares clustering problems
- Authors: Ordin, Burak , Bagirov, Adil
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 61, no. 2 (2015), p. 341-361
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
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- Description: Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k-means and modified global k-means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global k-means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the k-means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global k-means algorithms in finding global solutions to clustering problems.
A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization
- Authors: Long, Qiang , Wu, Changzhi
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 10, no. 4 (2014), p. 1279-1296
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- Description: A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimization problems only with box constraints. Then, the combination of genetic algorithm and Hooke-Jeeves method is applied to solve the transformed optimization problems. Since Hooke-Jeeves method is good at local search, our proposed method dramatically improves the accuracy and convergence rate of genetic algorithm. In view of the derivative-free of Hooke-Jeeves method, our method only requires information of objective function value which not only can overcome the computational difficulties caused by the ill-condition of the square penalty function, but also can handle the non-diffierentiability by the exact penalty function. Some well-known test problems are investigated. The numerical results show that our proposed method is eficient and robust.
A necessary optimality condition for free knots linear splines: Special cases
- Authors: Sukhorukova, Nadezda
- Date: 2010
- Type: Text , Journal article
- Relation: Pacific Journal of Optimization Vol. 6, no. 2, Suppl. 1 (2010), p. 305-317
- Full Text: false
- Description: In this paper, we study the problem of best Chebyshev approximation by linear splines. We construct linear splines as a max - min of linear functions. Then we apply nonsmooth optimisation techniques to analyse and solve the corresponding optimisation problems. This approach allows us to identify and introduce a new important property of linear spline knots (regular and irregular). Using this property, we derive a necessary optimality condition for the case of regular knots. This condition is stronger than those existing in the literature. We also present a numerical example which demonstrates the difference between the old and the new optimality conditions.
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
A new auxiliary function method for systems of nonlinear equations
- Authors: Wu, Zhiyou , Bai, Fusheng , Li, Guoquan , Yang, Yongjian
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 11, no. 2 (2014), p. 345-364
- Full Text: false
- Reviewed:
- Description: In this paper, we present a new global optimization method to solve nonlinear systems of equations. We reformulate given system of nonlinear equations as a global optimization problem and then give a new auxiliary function method to solve the reformulated global optimization problem. The new auxiliary function proposed in this paper can be a filled function, a quasifilled function or a strict filled function with appropriately chosen parameters. Several numerical examples are presented to illustrate the effciency of the present approach.
A new local and global optimization method for mixed integer quadratic programming problems
- Authors: Li, G. Q. , Wu, Zhiyou , Quan, Jing
- Date: 2010
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 217, no. 6 (2010), p. 2501-2512
- Full Text: false
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- Description: In this paper, a new local optimization method for mixed integer quadratic programming problems with box constraints is presented by using its necessary global optimality conditions. Then a new global optimization method by combining its sufficient global optimality conditions and an auxiliary function is proposed. Some numerical examples are also presented to show that the proposed optimization methods for mixed integer quadratic programming problems with box constraints are very efficient and stable. Crown Copyright © 2010.
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.
A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems
- Authors: Bagirov, Adil , Yearwood, John
- Date: 2006
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 170, no. 2 (2006), p. 578-596
- Full Text: false
- Reviewed:
- Description: The minimum sum-of-squares clustering problem is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the former problem based on nonsmooth optimization techniques is developed. The issue of applying this algorithm to large data sets is discussed. Results of numerical experiments have been presented which demonstrate the effectiveness of the proposed algorithm. © 2004 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001520
A new proof of Balinski's theorem on the connectivity of polytopes
- Authors: Pineda-Villavicencio, Guillermo
- Date: 2021
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 344, no. 7 (2021), p.
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- Description: Balinski (1961) proved that the graph of a d-dimensional convex polytope is d-connected. We provide a new proof of this result. Our proof provides details on the nature of a separating set with exactly d vertices; some of which appear to be new. © 2021 Elsevier B.V.
A note on primal-dual stability in infinite linear programming
- Authors: Goberna, Miguel , López, Marco , Ridolfi, Andrea , Vera de Serio, Virginia
- Date: 2020
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 14, no. 8 (2020), p. 2247-2263
- Full Text: false
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- Description: In this note we analyze the simultaneous preservation of the consistency (and of the inconsistency) of linear programming problems posed in infinite dimensional Banach spaces, and their corresponding dual problems, under sufficiently small perturbations of the data. We consider seven different scenarios associated with the different possibilities of perturbations of the data (the objective functional, the constraint functionals, and the right hand-side function), i.e., which of them are known, and remain fixed, and which ones can be perturbed because of their uncertainty. The obtained results allow us to give sufficient and necessary conditions for the coincidence of the optimal values of both problems and for the stability of the duality gap under the same type of perturbations. There appear substantial differences with the finite dimensional case due to the distinct topological properties of cones in finite and infinite dimensional Banach spaces. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
- Description: Funding details: Australian Research Council, ARC, DP180100602: http://purl.org/au-research/grants/arc/DP180100602
A novel error indicator and an adaptive refinement technique using the scaled boundary finite element method
- Authors: Song, Chongmin , Ooi, Ean Tat , Pramod, Aladurthi , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 94, no. (2018), p. 10-24
- Full Text: false
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- Description: In this paper, an adaptive refinement strategy based on the scaled boundary finite element method on quadtree meshes for linear elasticity problems is discussed. Within this framework, the elements with hanging nodes are treated as polygonal elements and thus does not require special treatment. The adaptive refinement is supplemented with a novel error indicator. The local error is estimated directly from the solution of the scaled boundary governing equations. The salient feature is that it does not require any stress recovery techniques. The efficacy and the robustness of the proposed approach are demonstrated with a few numerical examples.