共查询到20条相似文献,搜索用时 15 毫秒
1.
Alexander J. Zaslavski 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):952-970
In this work we study the structure of approximate solutions of an autonomous discrete-time control system with a compact metric space of states X which is a subset of a finite-dimensional Euclidean space. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous function v:Ω→R1 which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. Usually, in economic dynamics, the turnpike properties have been studied for systems such that all their good programs converge to a turnpike which was an interior point of Ω. In this paper we establish turnpike results for a large class of control systems for which the turnpike is not necessarily an interior point of Ω. 相似文献
2.
We consider local minimizers a domain in , of the variational integral with integrand f of upper (lower) growth rate q (s). We show using a lemma due to Frehse and Seregin that u has H?lder continuous first derivatives provided that .
Received: 2 October 2001 / Accepted: 25 October 2001 / Published online: 28 February 2002 相似文献
3.
Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics 总被引:2,自引:0,他引:2
Gianni Dal Maso Adriana Garroni 《Calculus of Variations and Partial Differential Equations》2008,31(2):137-145
In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the
jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of
the problem. 相似文献
4.
A. D. Ioffe R. T. Rockafellar 《Calculus of Variations and Partial Differential Equations》1996,4(1):59-87
Necessary conditions are developed for a general problem in the calculus of variations in which the Lagrangian function, although finite, need not be Lipschitz continuous or convex in the velocity argument. For the first time in such a broadly nonsmooth, nonconvex setting, a full subgradient version of Euler's equation is derived for an arc that furnishes a local minimum in the classical weak sense, and the Weierstrass inequality is shown to accompany it when the arc gives a local minimum in the strong sense. The results are achieved through new techniques in nonsmooth analysis.This research was supported in part by funds from the U.S.-Israel Science Foundation under grant 90-00455, and also by the Fund for the Promotion of Research at the Technion under grant 100-954 and by the U.S. National Science Foundation under grant DMS-9200303.This article was processed by the author using the
style filepljourlm from Springer-Verlag. 相似文献
5.
Summary. In this paper we study a numerical scheme for non-convex vector variational problems allowing for microstructure, based on
the approximation of gradient Young measures. We present a convergence result and some numerical experiments.
Received March 26, 2000 / Revised version received November 13, 2000 / Published online March 20, 2001 相似文献
6.
Lech Pasicki 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5678-5684
We apply an order reasoning to mappings satisfying the triangle inequality. This general approach yields the Ekeland’s variational principle as one of the consequences. In addition we obtain an extension of the Brøndsted variational principle and of the Takahashi fixed point theorem. 相似文献
7.
The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images. 相似文献
8.
Giulia Treu Mihai Vornicescu 《Calculus of Variations and Partial Differential Equations》2000,11(3):307-319
We consider the following problems
where is a convex function, is an open bounded subset of is a closed convex subset of such that and and are suitable obstacles. We give conditions on the function {\it g} under which the two problems are equivalent.
Received March 24, 1999/ Accepted January 14, 2000 / Published online June 28, 2000 相似文献
9.
《Optimization》2012,61(4):377-391
In this paper we examine the structure of extremals of variational problems with continuous integrands f:R n ?×?R n ?→?R 1 which belong to a complete metric space of functions. Our results deal with the turnpike properties of variational problems. To have this property means that the solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions. 相似文献
10.
In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of the solutions of the variational inequality problem by using a new hybrid method. We obtain a new result for finding a solution of an equilibrium problem and the solutions of the variational inequality problem. 相似文献
11.
B. Dacorogna I. Fonseca J. Malý K. Trivisa 《Calculus of Variations and Partial Differential Equations》1999,9(3):185-206
The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained
to remain on a
-dimensional manifold is obtained. If is a continuous function satisfying for and for all then where is open, bounded, and is the tangential quasiconvexification of f at
belong to the tangent space to at
Received October 10, 1998 / Accepted December 1, 1998 相似文献
12.
Jose-Luis Menaldi 《Acta Appl Math》1987,8(2):165-198
Optimal stopping and impulse control problems for degenerate diffusion with jumps are studied in this paper. Lipschitzian coefficients for the diffusion process, data with polynomial growth, and evolution in the whole space are the main assumptions on the models. Several characterizations of the optimal cost functions are given. Existence of optimal policies is obtained.This research has been supported in part by Army Research Office Contract DAAG29-83-K-0014 and by National Science Foundation Grant DMS-8601998. 相似文献
13.
Stefan Hildebrandt Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》1999,9(3):249-267
Let be a two-dimensional parametric variational integral the Lagrangian F(x,z) of which is positive definite and elliptic, and suppose that is a closed rectifiable Jordan curve in . We then prove that there is a conformally parametrized minimizer of in the class of surfaces of the type of the disk B which are bounded by . An immediate consequence of this theorem is that the Dirichlet integral and the area functional have the same infima, a
result whose proof usually requires a Lichtenstein-type mapping theorem or else Morrey's lemma on -conformal mappings. In addition we show that the minimizer of is H?lder continuous in B, and even in if satisfies a chord-arc condition. In Section 1 it is described how our results are related to classical investigations, in
particular to the work of Morrey. Without difficulty our approach can be carried over to two-dimensional surfaces of codimension
greater than one.
Received July 20, 1998 / Accepted October 23, 1998 相似文献
14.
In this paper we study mathematical programming problems with mixed constraints in a Banach space and show that most of the problems (in the Baire category sense) are well-posed. Our result is a generalization of a result of Ioffe et al. [SIAM J. Optim. 12 (2001) 461–478] obtained for finite-dimensional Banach spaces. 相似文献
15.
Prapairat JunlouchaiSomyot Plubtieng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):999-1004
In this paper, we prove the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over compact convex subsets in a reflexive Banach space with a Fréchet differentiable norm. Moreover, we give some conditions that guarantee the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over unbounded closed convex subsets. The result obtained in this paper improves and extends the recent ones announced by Yu and Yang [J. Yu, H. Yang, Existence of solutions for generalized variational inequality problems, Nonlinear Anal., 71 (2009) e2327-e2330] and many others. 相似文献
16.
Jun Kobayashi 《Journal of Functional Analysis》2004,214(2):428-449
Let X be a Banach space on which a symmetry group G linearly acts and let J be a G-invariant functional defined on X. In 1979, R. Palais (Comm. Math. Phys. 69 (1979) 19) gave some sufficient conditions to guarantee the so-called “Principle of Symmetric Criticality”: every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X. This principle is generalized to the case where J is not differentiable within the setting which does not require the full variational structure under the hypothesis that the action of G is isometry or G is compact. 相似文献
17.
Graziano Crasta 《Mathematische Zeitschrift》2000,235(3):569-589
We are concerned with the problem of existence, uniqueness and qualitative properties of solutions to the radially symmetric
variational problem
where is the ball of centered at the origin and with radius , the map is a normal integrand, and is a convex function of the second variable. This kind of problems, with non-convex lagrangians with respect to , arise in various fields of applied sciences, such as optimal design and nonlinear elasticity.
Received June 18, 1998; in final form August 26, 1999 / Published online September 14, 2000 相似文献
18.
Stefan Krömer 《Calculus of Variations and Partial Differential Equations》2008,32(2):219-236
We study functionals of the form
where u is a real valued function over the ball which vanishes on the boundary and W is nonconvex. The functional is assumed to be radially symmetric in the sense that W only depends on . Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation. Our
assumptions on G do not include convexity, thus extending a result of A. Cellina and S. Perrotta. 相似文献
19.
Chaichana Jaiboon 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1180-1202
In this paper, we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem (MEP), the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-inverse-strongly monotone mapping in Hilbert spaces. Furthermore, we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions, which solves some optimization problems. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab, Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl. 354 (2009) 319-329; Y. Yao, M. A. Noor, Y.C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479-509] and many others. 相似文献