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Journal articles on the topic 'Global minimizers'

Author: Grafiati

Published: 14 March 2023

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1

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

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2

Choksi, Rustum, Marco Morandotti, and Marco Veneroni. "Global minimizers for axisymmetric multiphase membranes." ESAIM: Control, Optimisation and Calculus of Variations 19, no. 4 (July 26, 2013): 1014–29. http://dx.doi.org/10.1051/cocv/2012042.

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3

Conti, Monica, and Veronica Felli. "Global minimizers of coexistence for competing species." Journal of the London Mathematical Society 83, no. 3 (March 2, 2011): 606–18. http://dx.doi.org/10.1112/jlms/jdq085.

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4

David, Guy. "Global minimizers of the Mumford-Shah function." Current Developments in Mathematics 1997, no. 1 (1997): 219–24. http://dx.doi.org/10.4310/cdm.1997.v1997.n1.a13.

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5

Leonetti, Francesco, and Francesco Siepe. "Global integrability for minimizers of anisotropic functionals." Manuscripta Mathematica 144, no. 1-2 (October 17, 2013): 91–98. http://dx.doi.org/10.1007/s00229-013-0641-y.

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6

Carrillo, José Antonio, Michel Chipot, and Yanghong Huang. "On global minimizers of repulsive–attractive power-law interaction energies." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2028 (November 13, 2014): 20130399. http://dx.doi.org/10.1098/rsta.2013.0399.

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We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations.

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7

DA LUZ, ADRIANA, and EZEQUIEL MADERNA. "On the free time minimizers of the NewtonianN-body problem." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 2 (November 26, 2013): 209–27. http://dx.doi.org/10.1017/s0305004113000650.

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AbstractIn this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. An example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice ofx0, there should be at least one free time minimizerx(t)defined for allt≥ 0 and satisfyingx(0)=x0. We prove that such motions are completely parabolic. Using Marchal's theorem we deduce as a corollary that there are no entire free time minimizers, i.e. defined on$\mathbb{R}$. This means that the Mañé set of the NewtonianN-body problem is empty.

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8

MRAMOR, BLAŽ, and BOB RINK. "A dichotomy theorem for minimizers of monotone recurrence relations." Ergodic Theory and Dynamical Systems 35, no. 1 (September 27, 2013): 215–48. http://dx.doi.org/10.1017/etds.2013.47.

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AbstractVariational monotone recurrence relations arise in solid state physics as generalizations of the Frenkel–Kontorova model for a ferromagnetic crystal. For such problems, Aubry–Mather theory establishes the existence of ‘ground states’ or ‘global minimizers’ of arbitrary rotation number. A nearest neighbor crystal model is equivalent to a Hamiltonian twist map. In this case, the global minimizers have a special property: they can only cross once. As a non-trivial consequence, every one of them has the Birkhoff property. In crystals with a larger range of interaction and for higher order recurrence relations, the single crossing property does not hold and there can exist global minimizers that are not Birkhoff. In this paper we investigate the crossings of global minimizers. Under a strong twist condition, we prove the following dichotomy: they are either Birkhoff, and thus very regular, or extremely irregular and non-physical: they then grow exponentially and oscillate. For Birkhoff minimizers, we also prove certain strong ordering properties that are well known for twist maps.

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9

Spector, Scott J. "Linear deformations as global minimizers in nonlinear elasticity." Quarterly of Applied Mathematics 52, no. 1 (March 1, 1994): 59–64. http://dx.doi.org/10.1090/qam/1262319.

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10

Speight, J. M., and M. Svensson. "SOME GLOBAL MINIMIZERS OF A SYMPLECTIC DIRICHLET ENERGY." Quarterly Journal of Mathematics 62, no. 3 (April 23, 2010): 737–45. http://dx.doi.org/10.1093/qmath/haq013.

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11

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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12

Gao, Hongya, Miaomiao Huang, and Wei Ren. "Global Regularity for Minimizers of Some Anisotropic Variational Integrals." Journal of Optimization Theory and Applications 188, no. 2 (January 8, 2021): 523–46. http://dx.doi.org/10.1007/s10957-020-01795-7.

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13

Schröder, Jan Philipp. "Global minimizers for Tonelli Lagrangians on the 2-torus." Journal of Topology and Analysis 07, no. 02 (March 26, 2015): 261–91. http://dx.doi.org/10.1142/s1793525315500090.

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We study action-minimizing orbits in Tonelli Lagrangian systems on the 2-torus on fixed energy levels above Mañé's strict critical value. Our work generalizes the results of Morse, Hedlund and Bangert on minimal geodesics in Riemannian 2-tori. The techniques in the proofs involve classical variational ones, as well as the theories of Mather, Mañé and Fathi, which allow the step from reversible to non-reversible dynamics.

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14

Cristofari, Andrea, Tayebeh Dehghan Niri, and Stefano Lucidi. "On global minimizers of quadratic functions with cubic regularization." Optimization Letters 13, no. 6 (August 23, 2018): 1269–83. http://dx.doi.org/10.1007/s11590-018-1316-0.

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15

Foss, M. "Global regularity for almost minimizers of nonconvex variational problems." Annali di Matematica Pura ed Applicata 187, no. 2 (May 5, 2007): 263–321. http://dx.doi.org/10.1007/s10231-007-0045-2.

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16

Nikolova, Mila. "Description of the Minimizers of Least Squares Regularized with $\ell_0$-norm. Uniqueness of the Global Minimizer." SIAM Journal on Imaging Sciences 6, no. 2 (January 2013): 904–37. http://dx.doi.org/10.1137/11085476x.

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17

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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18

LAMI DOZO, ENRIQUE J., and OLAF TORNÉ. "SYMMETRY AND SYMMETRY BREAKING FOR MINIMIZERS IN THE TRACE INEQUALITY." Communications in Contemporary Mathematics 07, no. 06 (December 2005): 727–46. http://dx.doi.org/10.1142/s0219199705001921.

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We consider symmetry properties of minimizers in the variational characterization of the best constant in the trace inequality [Formula: see text] in the ball Bρ of radius ρ. When p is fixed, minimizers in this problem can be radial or non-radial depending on the parameters q and ρ. We prove that there is a global radial function u0 > 0, with u0 independent of q, such that any radial minimizer is a multiple of the restriction of u0 to Bρ. Next, we prove that if either q or ρ is sufficiently large, then the minimizers are non-radial. In the case when p = 2, we consider a generalization of the minimization problem and improve some of the above symmetry results. We also present some numerical results describing the exact values of q and ρ for which radial symmetry breaking occurs.

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19

Bandegi, Mahdi, and David Shirokoff. "Approximate Global Minimizers to Pairwise Interaction Problems via Convex Relaxation." SIAM Journal on Applied Dynamical Systems 17, no. 1 (January 2018): 417–56. http://dx.doi.org/10.1137/16m1069146.

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20

Zhang, Shan, Zuhan Liu, and Zhigui Lin. "Global minimizers of coexistence for rotating -component Bose–Einstein condensates." Nonlinear Analysis: Real World Applications 12, no. 5 (October 2011): 2567–78. http://dx.doi.org/10.1016/j.nonrwa.2011.03.006.

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21

Porretta, Alessio. "On the regularity of the total variation minimizers." Communications in Contemporary Mathematics 23, no. 01 (November 20, 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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22

Parsopoulos, K. E., and M. N. Vrahatis. "On the Computation of All Global Minimizers Through Particle Swarm Optimization." IEEE Transactions on Evolutionary Computation 8, no. 3 (June 2004): 211–24. http://dx.doi.org/10.1109/tevc.2004.826076.

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23

Chan, Tony F., Selim Esedoglu, and Mila Nikolova. "Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models." SIAM Journal on Applied Mathematics 66, no. 5 (January 2006): 1632–48. http://dx.doi.org/10.1137/040615286.

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24

Lemenant, Antoine. "A rigidity result for global Mumford–Shah minimizers in dimension three." Journal de Mathématiques Pures et Appliquées 103, no. 4 (April 2015): 1003–23. http://dx.doi.org/10.1016/j.matpur.2014.10.002.

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25

Liu, Yong, Kelei Wang, and Juncheng Wei. "Global minimizers of the Allen–Cahn equation in dimension n≥ 8." Journal de Mathématiques Pures et Appliquées 108, no. 6 (December 2017): 818–40. http://dx.doi.org/10.1016/j.matpur.2017.05.006.

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26

Habermann, J. "Global gradient estimates for non-quadratic vector-valued parabolic quasi-minimizers." Nonlinear Analysis: Theory, Methods & Applications 114 (February 2015): 42–73. http://dx.doi.org/10.1016/j.na.2014.10.014.

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27

Choksi, Rustum. "On global minimizers for a variational problem with long-range interactions." Quarterly of Applied Mathematics 70, no. 3 (September 1, 2012): 517–37. http://dx.doi.org/10.1090/s0033-569x-2012-01316-9.

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28

Almog, Yaniv, Leonid Berlyand, Dmitry Golovaty, and Itai Shafrir. "Global minimizers for a p-Ginzburg–Landau-type energy in R2." Journal of Functional Analysis 256, no. 7 (April 2009): 2268–90. http://dx.doi.org/10.1016/j.jfa.2008.09.020.

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29

Miao, Xue-Qing, Ya-Nan Wang, and Wen-Xin Qin. "Minimizers with Bounded Action for the High-Dimensional Frenkel–Kontorova Model." International Journal of Bifurcation and Chaos 25, no. 08 (July 2015): 1550098. http://dx.doi.org/10.1142/s0218127415500984.

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In Aubry–Mather theory for monotone twist maps or for one-dimensional Frenkel–Kontorova (FK) model with nearest neighbor interactions, each global minimizer (minimal energy configuration) is naturally Birkhoff. However, this is not true for the one-dimensional FK model with non-nearest neighbor interactions or for the high-dimensional FK model. In this paper, we study the Birkhoff property of minimizers with bounded action for the high-dimensional FK model.

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30

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 (June 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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31

Chen, Xi, Yi-rong Yao, and Quan Zheng. "Finite-dimensional approximation to global minimizers in functional spaces with R-convergence." Applied Mathematics and Mechanics 32, no. 1 (January 2011): 107–18. http://dx.doi.org/10.1007/s10483-011-1398-8.

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32

Fiaschi, Alice, Dorothee Knees, and Sina Reichelt. "Global higher integrability of minimizers of variational problems with mixed boundary conditions." Journal of Mathematical Analysis and Applications 401, no. 1 (May 2013): 269–88. http://dx.doi.org/10.1016/j.jmaa.2012.11.040.

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33

Bedrossian, Jacob. "Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion." Applied Mathematics Letters 24, no. 11 (November 2011): 1927–32. http://dx.doi.org/10.1016/j.aml.2011.05.022.

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34

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 (January 4, 2012): 673–718. http://dx.doi.org/10.1007/s10231-011-0243-9.

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35

Canarius, Thomas, and Reiner Schätzle. "Finiteness and Positivity Results for Global Minimizers of a Semilinear Elliptic Problem." Journal of Differential Equations 148, no. 1 (September 1998): 212–29. http://dx.doi.org/10.1006/jdeq.1998.3457.

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36

Shen, Peiping, and Yanjun Wang. "A new pruning test for finding all global minimizers of nonsmooth functions." Applied Mathematics and Computation 168, no. 2 (September 2005): 739–55. http://dx.doi.org/10.1016/j.amc.2004.09.050.

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37

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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38

Fujishima, Yohei, and Jens Habermann. "Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces." Advances in Calculus of Variations 10, no. 3 (July 1, 2017): 267–301. http://dx.doi.org/10.1515/acv-2015-0038.

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AbstractWe prove up-to-the-boundary higher integrability estimates for parabolic quasi-minimizers on a domain \Omega_{T}= Ω \times (0,T), where Ω denotes an open domain in a doubling metric measure space which supports a Poincaré inequality. The higher integrability for upper gradients is shown globally and under optimal conditions on the boundary \partialΩ of the domain as well as on the boundary data itself. This is a starting point for a further discussion on parabolic quasi-minima on metric measure spaces, such as for example regularity or stability issues.

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39

Giorgi, T., and R. G. Smits. "Remarks on the existence of global minimizers for the Ginzburg–Landau energy functional." Nonlinear Analysis: Theory, Methods & Applications 53, no. 2 (April 2003): 147–55. http://dx.doi.org/10.1016/s0362-546x(01)00800-8.

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40

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 (September 2003): 2337–51. http://dx.doi.org/10.1016/s0045-7949(03)00313-4.

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41

Sandier, Etienne, and Sylvia Serfaty. "Global minimizers for the Ginzburg–Landau functional below the first critical magnetic field." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 17, no. 1 (January 2000): 119–45. http://dx.doi.org/10.1016/s0294-1449(99)00106-7.

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42

Almog, Yaniv, Leonid Berlyand, Dmitry Golovaty, and Itai Shafrir. "On the limitp→∞of global minimizers for a p -Ginzburg–Landau-type energy." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 30, no. 6 (November 2013): 1159–74. http://dx.doi.org/10.1016/j.anihpc.2012.12.013.

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43

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 (August 2000): 385–404. http://dx.doi.org/10.1142/s0219199700000190.

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44

Li, Mei Xia. "A Class of Augumented Lagrangian Function for Nonlinear Programming." Advanced Materials Research 271-273 (July 2011): 1955–60. http://dx.doi.org/10.4028/www.scientific.net/amr.271-273.1955.

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In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

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45

Sattarzadeh, A. R., and H. Mohebi. "Characterizing approximate global minimizers of the difference of two abstract convex functions with applications." Filomat 33, no. 8 (2019): 2431–45. http://dx.doi.org/10.2298/fil1908431s.

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In this paper, we first investigate characterizations of maximal elements of abstract convex functions under a mild condition. Also, we give various characterizations for global "-minimum of the difference of two abstract convex functions and, by using the abstract Rockafellar?s antiderivative, we present the abstract ?-subdifferential of abstract convex functions in terms of their abstract subdifferential. Finally, as an application, a necessary and sufficient condition for global ?-minimum of the difference of two increasing and positively homogeneous (IPH) functions is presented.

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46

Ding, Shijin, and Qiang Du. "The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films." Communications on Pure & Applied Analysis 1, no. 3 (2002): 327–40. http://dx.doi.org/10.3934/cpaa.2002.1.327.

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47

Taati, Akram, and Maziar Salahi. "On Local Non-Global Minimizers of Quadratic Optimization Problem with a Single Quadratic Constraint." Numerical Functional Analysis and Optimization 41, no. 8 (March 10, 2020): 969–1005. http://dx.doi.org/10.1080/01630563.2020.1733605.

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48

Byun, Sun-Sig, Jihoon Ok, and Yeonghun Youn. "Global gradient estimates for spherical quasi-minimizers of integral functionals with p(x)-growth." Nonlinear Analysis 177 (December 2018): 186–208. http://dx.doi.org/10.1016/j.na.2018.01.017.

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49

DÁVILA, JUAN. "GLOBAL REGULARITY FOR A SINGULAR EQUATION AND LOCAL H1 MINIMIZERS OF A NONDIFFERENTIABLE FUNCTIONAL." Communications in Contemporary Mathematics 06, no. 01 (February 2004): 165–93. http://dx.doi.org/10.1142/s0219199704001240.

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We prove optimal Hölder estimates up to the boundary for the maximal solution of a singular elliptic equation. The techniques used in this argument are applied to show that in some situations the maximal solution is a local minimizer of the corresponding functional in the topology of H1.

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50

Li, Xinrong, Naihua Xiu, and Shenglong Zhou. "Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers." Journal of Optimization Theory and Applications 184, no. 3 (December 9, 2019): 895–930. http://dx.doi.org/10.1007/s10957-019-01606-8.

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