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Relevant bibliographies by topics / Local/Global minimizers

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Journal articles

Academic literature on the topic 'Local/Global minimizers'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Local/Global minimizers"

1

Giner, E. "Local minimizers of integral functionals are global minimizers." Proceedings of the American Mathematical Society 123, no. 3 (1995): 755. http://dx.doi.org/10.1090/s0002-9939-1995-1254839-1.

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2

Jimbo, Shuichi, and Jian Zhai. "Domain perturbation method and local minimizers to Ginzburg-Landau functional with magnetic effect." Abstract and Applied Analysis 5, no. 2 (2000): 101–12. http://dx.doi.org/10.1155/s1085337500000233.

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We prove the existence of vortex local minimizers to Ginzburg-Landau functional with a global magnetic effect. A domain perturbating method is developed, which allows us to extend a local minimizer on a nonsimply connected superconducting material to the local minimizer with vortex on a simply connected material.

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3

Andersson, Mats, Oleg Burdakov, Hans Knutsson, and Spartak Zikrin. "Global Search Strategies for Solving Multilinear Least-Squares Problems." Sultan Qaboos University Journal for Science [SQUJS] 16 (April 1, 2012): 12. http://dx.doi.org/10.24200/squjs.vol17iss1pp12-21.

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The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by the results of numerical experiments performed for some problems related to the design of filter networks.

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4

Rodríguez, Nancy, and Yi Hu. "On the steady-states of a two-species non-local cross-diffusion model." Journal of Applied Analysis 26, no. 1 (2020): 1–19. http://dx.doi.org/10.1515/jaa-2020-2003.

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AbstractWe investigate the existence and properties of steady-state solutions to a degenerate, non-local system of partial differential equations that describe two-species segregation in homogeneous and heterogeneous environments. This is accomplished via the analysis of the existence and non-existence of global minimizers to the corresponding free energy functional. We prove that in the spatially homogeneous case global minimizers exist if and only if the mass of the potential governing the intra-species attraction is sufficiently large and the support of the potential governing the interspecies repulsion is bounded. Moreover, when they exist they are such that the two species have disjoint support, leading to complete segregation. For the heterogeneous environment we show that if a sub-additivity condition is satisfied then global minimizers exists. We provide an example of an environment that leads to the sub-additivity condition being satisfied. Finally, we explore the bounded domain case with periodic conditions through the use of numerical simulations.

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5

Palatucci, Giampiero, Ovidiu Savin, and Enrico Valdinoci. "Local and global minimizers for a variational energy involving a fractional norm." Annali di Matematica Pura ed Applicata 192, no. 4 (2012): 673–718. http://dx.doi.org/10.1007/s10231-011-0243-9.

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6

Porretta, Alessio. "On the regularity of the total variation minimizers." Communications in Contemporary Mathematics 23, no. 01 (2019): 1950082. http://dx.doi.org/10.1142/s0219199719500822.

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We prove regularity results for the unique minimizer of the total variation functional, currently used in image processing analysis since the work by Rudin, Osher and Fatemi. In particular, we show that if the source term [Formula: see text] is locally (respectively, globally) Lipschitz, then the solution has the same regularity with local (respectively, global) Lipschitz norm estimated accordingly. The result is proved in any dimension and for any (regular) domain. So far we extend a similar result proved earlier by Caselles, Chambolle and Novaga for dimension [Formula: see text] and (in case of the global regularity) for convex domains.

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7

Teughels, Anne, Guido De Roeck, and Johan A. K. Suykens. "Global optimization by coupled local minimizers and its application to FE model updating." Computers & Structures 81, no. 24-25 (2003): 2337–51. http://dx.doi.org/10.1016/s0045-7949(03)00313-4.

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8

AZORERO, J. P. GARCÍA, I. PERAL ALONSO, and JUAN J. MANFREDI. "SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS." Communications in Contemporary Mathematics 02, no. 03 (2000): 385–404. http://dx.doi.org/10.1142/s0219199700000190.

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9

Enkhbat, R., and T. Bayartugs. "Quasiconvex Semidefinite Minimization Problem." Journal of Optimization 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/346131.

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We introduce so-called semidefinite quasiconvex minimization problem. We derive new global optimality conditions for the above problem. Based on the global optimality conditions, we construct an algorithm which generates a sequence of local minimizers which converge to a global solution.

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10

Duboscq, Romain, and Olivier Pinaud. "On local quantum Gibbs states." Journal of Mathematical Physics 63, no. 10 (2022): 102102. http://dx.doi.org/10.1063/5.0058574.

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We address in this work the problem of minimizing quantum entropies under local constraints. We suppose that macroscopic quantities, such as the particle density, current, and kinetic energy, are fixed at each point of [Formula: see text] and look for a density operator over [Formula: see text], minimizing an entropy functional. Such minimizers are referred to as local Gibbs states. This setting is in contrast with the classical problem of prescribing global constraints, where the total number of particles, total current, and total energy in the system are fixed. The question arises, for instance, in the derivation of fluid models from quantum dynamics. We prove, under fairly general conditions, that the entropy admits a unique constrained minimizer. Due to a lack of compactness, the main difficulty in the proof is to show that limits of minimizing sequences satisfy the local energy constraint. We tackle this issue by introducing a simpler auxiliary minimization problem and by using a monotonicity argument involving the entropy.

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