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  • 1
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    Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques (2012)
    Springer
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    Publication Date: 2012-03-27
    Description:    This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered. Content Type Journal Article Pages 1-24 DOI 10.1007/s10957-012-0022-9 Authors Ionela Prodan, Automatic Control Department, SUPELEC Systems Sciences (E3S), Gif sur Yvette, France Florin Stoican, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway Sorin Olaru, Automatic Control Department, SUPELEC Systems Sciences (E3S), Gif sur Yvette, France Silviu-Iulian Niculescu, Laboratory of Signal and Systems, CNRS-SUPELEC, Gif sur Yvette, France Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
    Print ISSN: 0022-3239
    Electronic ISSN: 1573-2878
    Topics: Mathematics
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  • 2
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    Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems (2011)
    Springer
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    Publication Date: 2011-06-15
    Description:    We introduce a gradient descent algorithm for solving large scale unconstrained nonlinear optimization problems. The computation of the initial trial steplength is based on the usage of both the quasi-Newton property and the Hessian inverse approximation by an appropriate scalar matrix. The nonmonotone line search technique for the steplength calculation is applied later. The computational and storage complexity of the new method is equal to the computational and storage complexity of the Barzilai and Borwein method. On the other hand, the reported numerical results indicate improvements in favor of the new method with respect to the well known global Barzilai and Borwein method. Content Type Journal Article Pages 1-17 DOI 10.1007/s10957-011-9864-9 Authors Marko Miladinović, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia Predrag Stanimirović, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia Sladjana Miljković, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 3
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    On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations (2011)
    Springer
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    Publication Date: 2011-06-25
    Description:    We present a modified method for solving nonlinear systems of equations with order of convergence higher than other competitive methods. We generalize also the efficiency index used in the one-dimensional case to several variables. Finally, we show some numerical examples, where the theoretical results obtained in this paper are applied. Content Type Journal Article Pages 1-12 DOI 10.1007/s10957-011-9870-y Authors J. A. Ezquerro, Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004 Logroño, Spain M. Grau-Sánchez, Department of Applied Mathematics II, Technical University of Catalonia, Jordi Girona 1-3, Omega, 08034 Barcelona, Spain A. Grau, Department of Applied Mathematics II, Technical University of Catalonia, Jordi Girona 1-3, Omega, 08034 Barcelona, Spain M. A. Hernández, Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004 Logroño, Spain M. Noguera, Department of Applied Mathematics II, Technical University of Catalonia, Jordi Girona 1-3, Omega, 08034 Barcelona, Spain N. Romero, Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004 Logroño, Spain Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 4
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    Blaschke-Type Theorem and Separation of Disjoint Closed Geodesic Convex Sets (2011)
    Springer
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    Publication Date: 2011-06-25
    Description:    In this paper, we deal with analytic and geometrical properties of geodesic convex sets and geodesic paths. We show that Blaschke’s Theorem for convex sets is also true for geodesic convex sets and geodesic paths in a simple polygon. Some geometrical properties of geodesic triangles are presented. Furthermore, separation of geodesic convex sets is shown. Content Type Journal Article Pages 1-11 DOI 10.1007/s10957-011-9868-5 Authors N. N. Hai, Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam P. T. An, CEMAT, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 5
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    Uniform Global Convergence of a Hybrid Scheme for Singularly Perturbed Reaction–Diffusion Systems (2011)
    Springer
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    Publication Date: 2011-06-25
    Description:    We consider a system of coupled singularly perturbed reaction–diffusion two-point boundary-value problems. A hybrid difference scheme on a piecewise-uniform Shishkin mesh is constructed for solving this system, which generates better approximations to the exact solution than the classical central difference scheme. Moreover, we prove that the method is third order uniformly convergent in the maximum norm when the singular perturbation parameter is small. Numerical experiments are conducted to validate the theoretical results. Content Type Journal Article Pages 1-15 DOI 10.1007/s10957-011-9867-6 Authors S. C. S. Rao, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India S. Kumar, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India M. Kumar, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 6
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    The Existence of Optimal Solution for a Shape Optimization Problem on Starlike Domain (2011)
    Springer
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    Publication Date: 2011-06-27
    Description:    In this paper, a shape optimization problem over a multi-dimensional starlike domain with boundary payoff is considered. The function, which characterizes the boundary of the domain with respect to some ball contained inside domain, is shown to be Lipschitz continuous. The existence of an optimal solution is proved. Content Type Journal Article Pages 1-10 DOI 10.1007/s10957-011-9878-3 Authors Y. He, School of Mathematics, Central South University, Changsha, 410075 China B. Z. Guo, Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190 China Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 7
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    Optimal Control Problems for Evolution Equations of Parabolic Type with Nonlinear Perturbations (2011)
    Springer
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    Publication Date: 2011-06-21
    Description:    In this paper, we study the optimal control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under Lipschitz continuity condition of the nonlinear term, we can obtain the optimal conditions and maximal principles for a given equation, which are described by the adjoint state corresponding to the given equation without the rigorous conditions for the nonlinear term. Content Type Journal Article Pages 1-16 DOI 10.1007/s10957-011-9866-7 Authors Jin-Mun Jeong, Department of Applied Mathematics, Pukyong National University, Busan, 608-737 South Korea Eun-Young Ju, Department of Applied Mathematics, Pukyong National University, Busan, 608-737 South Korea Su-Jin Cheon, Department of Applied Mathematics, Pukyong National University, Busan, 608-737 South Korea Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 8
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    Equivalence of Minimal ℓ0- and ℓp-Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p (2011)
    Springer
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    Publication Date: 2011-06-21
    Description:    For a bounded system of linear equalities and inequalities, we show that the NP-hard ℓ 0 -norm minimization problem is completely equivalent to the concave ℓ p -norm minimization problem, for a sufficiently small p . A local solution to the latter problem can be easily obtained by solving a provably finite number of linear programs. Computational results frequently leading to a global solution of the ℓ 0 -minimization problem and often producing sparser solutions than the corresponding ℓ 1 -solution are given. A similar approach applies to finding minimal ℓ 0 -solutions of linear programs. Content Type Journal Article Pages 1-10 DOI 10.1007/s10957-011-9871-x Authors G. M. Fung, R&D Clinical Systems, Siemens Medical Solutions, Inc., Malvern, PA, USA O. L. Mangasarian, Computer Sciences Department, University of Wisconsin, Madison, WI, USA Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 9
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    Local Linear Convergence of an Outer Approximation Projection Method for Variational Inequalities (2011)
    Springer
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    Publication Date: 2011-06-27
    Description:    This paper considers an outer approximation projection method for variational inequalities, in which the projections are not performed on the original set that appears in the variational inequality, but on a polyhedral convex set defined by the linearized constraints. It shows that the method converges linearly, when the starting point is sufficiently close to the solution and the step lengths are sufficiently small. Content Type Journal Article Pages 1-12 DOI 10.1007/s10957-011-9873-8 Authors Shu Lu, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA Sudhanshu Singh, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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  • 10
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    A Class of Linearized Proximal Alternating Direction Methods (2011)
    Springer
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    Publication Date: 2011-06-27
    Description:    Due to its significant efficiency, the alternating direction method (ADM) has attracted a lot of attention in solving linearly constrained structured convex optimization. In this paper, in order to make implementation of ADM relatively easy, some linearized proximal ADMs are proposed and the associated convergence results of the proposed linearized proximal ADMs are given. Additionally, theoretical analysis shows that the relaxation factor for the linearized proximal ADMs can have the same restriction region as that for the general ADM. Content Type Journal Article Pages 1-17 DOI 10.1007/s10957-011-9876-5 Authors M. H. Xu, School of Mathematics and Physics, Changzhou University, Changzhou, 213164 P.R. China T. Wu, Department of Mathematics, Nanjing University, Nanjing, 210093 P.R. China Journal Journal of Optimization Theory and Applications Online ISSN 1573-2878 Print ISSN 0022-3239
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    Topics: Mathematics
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