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1.
The approach to optimal control problems based on a purely variational reformulation may lead to new existence results by
using fine, general existence theorems for variational problems without convexity assumptions. We illustrate this perspective
here for autonomous one-dimensional problems and defer the study of more complex situations to later work.
This research was supported by Project MTM2004-07114 from Ministerio de Educación y Ciencia (Spain) and by Grant PAI05-029
from JCCM (Castilla-La Mancha). 相似文献
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R. Andreani C. E. Echagüe M. L. Schuverdt 《Journal of Optimization Theory and Applications》2010,146(2):255-266
The constant-rank condition for feasible points of nonlinear programming problems was defined by Janin (Math. Program. Study
21:127–138, 1984). In that paper, the author proved that the constant-rank condition is a first-order constraint qualification. In this work,
we prove that the constant-rank condition is also a second-order constraint qualification. We define other second-order constraint
qualifications. 相似文献
4.
Abadie Constraint Qualifications for Convex Constraint Systems and Applications to Calmness Property
In this paper, we mainly study concepts of Abadie constraint qualification and strong Abadie constraint qualification for a convex constraint system defined by a closed convex multifunction and a closed convex subset. These concepts can cover Abadie constraint qualifications for the feasible region of convex optimization problem and the convex multifunction. Several characterizations for these Abadie constraint qualifications are also provided. As applications, we use these Abadie constraint qualifications to characterize calmness properties of the convex constraint system. 相似文献
5.
Goeleven D. Miettinen M. Panagiotopoulos P. D. 《Journal of Optimization Theory and Applications》1999,103(3):567-601
Dynamic hemivariational inequalities are studied in the present paper. Starting from their solution in the distributional sense, we give certain existence and approximation results by using the Faedo–Galerkin method and certain compactness arguments. Applications from mechanics (viscoelasticity) illustrate the theory. 相似文献
6.
V. Jeyakumar 《Journal of Optimization Theory and Applications》2008,136(1):31-41
In convex optimization, a constraint qualification (CQ) is an essential ingredient for the elegant and powerful duality theory.
Various constraint qualifications which are sufficient for the Lagrangian duality have been given in the literature. In this
paper, we present constraint qualifications which characterize completely the Lagrangian duality. 相似文献
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Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten. 相似文献
9.
Xin Tao YE Chong LI 《数学学报(英文版)》2007,23(1):65-76
The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided. 相似文献
10.
On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case 总被引:2,自引:0,他引:2
Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn–Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated. 相似文献
11.
刘培德 《数学物理学报(A辑)》2010,30(5):1292-1305
弱型空间是近年来调和分析与鞅论中倍受关注的研究方向, 该文就以下几方面介绍有关弱型鞅空间的研究工作:(1) Lorentz鞅空间的原子分解;(2) Orlicz鞅空间的强弱型加权不等式; (3) 弱Orlicz鞅空间与拟范数不等式; (4) 在Banach空间理论与二进域调和分析中的应用. 相似文献
12.
含剩余对称平均的不等式及其应用 总被引:2,自引:0,他引:2
定义 n个正实数 x1,x2 ,… ,xn的剩余对称平均 ∑k ( x) ,借助于数学归纳法及优超理论证明当 x∈Rn+ + 时有 :∑2 ( x)≥ ∑3( x)≥…≥ ∑n ( x)≥ A( x) .并将此结果用于正定矩阵 ,n维长方体及单形 . 相似文献
13.
By means of a Carleman estimate, we obtain several observability inequalities by internal observation for hyperbolic equations with lower-order terms. Also, we apply our observability results to an exact controllability problem and an inverse wave source problem. 相似文献
14.
我们根据一般化凸空间上的KKM型定理得到了截口定理,然后作为它的应用讨论了若干个择一不等式.最后,引进了一个具体的一般化凸空间并在该空间上讨论了择一不等式解的存在性问题. 相似文献
15.
On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification 总被引:1,自引:0,他引:1
R. Andreani J. M. Martinez M. L. Schuverdt 《Journal of Optimization Theory and Applications》2005,125(2):473-483
The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors conjectured that the CPLD could be a constraint qualification. This conjecture is proven in the present paper. Moreover, it is shown that the CPLD condition implies the quasinormality constraint qualification, but that the reciprocal is not true. Relations with other constraint qualifications are given.This research has been supported by PRONEX-Optimization Grant 76.79.1008-00, by FAPESP Grants 01-04597-4 and 02-00832-1, and by CNPq. The authors are indebted to two anonymous referees for useful comments and to Prof. Liqun Qi for encouragement. 相似文献
16.
Monica Bianchi Enrico Miglierina Elena Molho Rita Pini 《Set-Valued and Variational Analysis》2013,21(1):47-65
Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem defined via m convex C 1,1 objective functions on a given closed ball in ? n . Two approaches are proposed: the first one adopts a local point of view around a given solution point, whereas the second one considers the solution set as a whole. A comparison between the two notions of well-conditioned problem is developed. We underline that both the condition numbers introduced in the present work reduce to the same condition number proposed by Zolezzi in 2003, in the special case of the scalar optimization problem considered there. A pseudodistance between functions is defined such that the condition number provides an upper bound on how far from a well–conditioned function f a perturbed function g can be chosen in order that g is well–conditioned too. For both the local and the global approach an extension of classical Eckart–Young distance theorem is proved, even if only a special class of perturbations is considered. 相似文献
17.
Mevlüt Tunç 《Mediterranean Journal of Mathematics》2014,11(4):1047-1059
In this study, the author establishes some inequalities of Hadamard-like based on convex and s-convexity in the second sense. Some applications to special means of positive real numbers are also given. 相似文献
18.
For the cohomology of a sheaf of Abelian groups with involution on a topological space, inequalities that are analogs of the classical Harnack--Thom inequality for the cohomology of a topological space with involution are proved. The general inequalities obtained are applied to reprove some known inequalities and prove new ones. 相似文献
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吴善和 《数学的实践与认识》2006,36(3):217-224
给出一类新的R adon型不等式,它们在代数不等式研究中有着广泛的应用,利用它们可直接得到一大批新的分式型不等式,也可运用它们证明或推广许多不等式. 相似文献