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1.
给出两种两个凸多面体差的表达式,利用这些表达式,可以具体计算这两种凸多面体的差,做为应用讨论了利用拟微分计算Penot微分和Clarke广义梯度,特别讨论了一类非光滑函数,极大值函数的光滑复合。 相似文献
2.
Representation of the Clarke subdifferential for a regular quasidifferentiable function 总被引:2,自引:0,他引:2
A class of Lipschitz quasidifferentiable functions is described for which the exact representation of the Clarke subdifferential in terms of a quasidifferential holds. The sufficient conditions formulated are different from those previously established by Rubinov and Akhundov. 相似文献
3.
We calculate the Clarke and Michel-Penot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via the generalized directional derivatives of the eigenvalue function, thereby completing earlier studies on the classical directional derivative. 相似文献
4.
讨论了不等式约束优化问题中拟微分形式下Fritz John必要条件与 Clarke广义梯度形式下Fritz John必要条件的关系.在较弱条件下给出了具有等式与不等式约束条件的两个Lagrange乘子形式的最优性必要条件,在这两个条件中等式约束函数的拟微分和Clarke广义梯度分别被使用。 相似文献
5.
Representative of Quasidifferentials and Its Formula for a Quasidifferentiable Function 总被引:1,自引:0,他引:1
Yan Gao 《Set-Valued Analysis》2005,13(4):323-336
The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia
proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalent class
of quasidifferentials. In the 2-dimensional case, the existence of the kernelled quasidifferential was shown. In this paper,
the existence of the kernelled quasidifferential in the n-dimensional space (n>2) is proved under the assumption that the Minkowski difference and the Demyanov difference of subdifferential and minus
superdifferential coincide. In particular, given a quasidifferential, the kernelled quasidifferential can be formulated. Applications
to two classes of generalized separable quasidifferentiable functions are developed.
Mathematics Subject Classifications (2000) 49J52, 54C60, 90C26.
This work was supported by Shanghai Education Committee (04EA01). 相似文献
6.
In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix. Absolutely symmetric functions are invariant under permutations and sign changes of its arguments. We extend previous work on subgradients to analogous formulae for the proximal subdifferential and Clarke subdifferential when the function is either locally Lipschitz or just lower semicontinuous. We illustrate the results by calculating the various subdifferentials of individual singular values. Another application gives a nonsmooth proof of Lidskii’s theorem for weak majorization.
Mathematics Subject Classifications (2000) Primary 90C31, 15A18; secondary 49K40, 26B05.Research supported by NSERC. 相似文献
7.
讨论了凸函数的次微分映射和凸集的支撑点集之间的内在关系,由此本给出了由凸函数的次微分映射所刻划的一个精细的Bishop-Phelps定理. 相似文献
8.
Y. Gao 《Journal of Optimization Theory and Applications》2006,130(3):431-442
Formulas of the differences of polyhedra in matrix space are proposed. Based on these formulas, the differences of polyhedra can be calculated by solving systems of linear inequalities. A modified algorithm for calculating one element of the differences is presented also. The motivation for this work is to compute the Clarke generalized Jacobian, the B-differential, and one of their elements via the quasidifferential. Applications to Newton methods for solving nonsmooth equations are discussed.This project was sponsored by the Shanghai Education Committee, Grant 04EA01, by the Education Ministry of China, and by the Shanghai Government, Grant T0502. The author thanks two anonymous referees and Professor F. Giannessi for valuable suggestions and comments. 相似文献
9.
We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens. 相似文献
10.
Leszek Gasiński 《Mathematische Nachrichten》2008,281(12):1728-1746
In this paper we consider quasilinear hemivariational inequality at resonance. We prove existence results for strongly resonant quasilinear problem, resonant problem under a Tang‐type condition as well as two multiplicity results. The method of the proofs is based on the nonsmooth critical point theory for locally Lipschitz functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
AbstractNecessary optimality conditions for local Henig efficient and superefficient solutions of vector equilibrium problems involving equality, inequality, and set constraints in Banach space with locally Lipschitz functions are established under a suitable constraint qualification via the Michel–Penot subdifferentials. With assumptions on generalized convexity, necessary conditions for Henig efficiency and superefficiency become sufficient ones. Some applications to vector variational inequalities and vector optimization problems are given as well. 相似文献
12.
Marián Fabian Philip D. Loewen Boris S. Mordukhovich 《Journal of Mathematical Analysis and Applications》2006,322(2):787-795
We extend the definition of the limiting Fréchet subdifferential and the limiting Fréchet normal cone from Asplund spaces to Asplund generated spaces. Then we prove a sum rule, a mean value theorem, and other statements for this concept. 相似文献
13.
We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in
n
. From this representation we obtain Banach–Mazur distance and volume ratio estimates. 相似文献
14.
Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems 总被引:1,自引:0,他引:1
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Czechoslovak Mathematical Journal》2004,54(2):347-371
In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)). 相似文献
15.
《Optimization》2012,61(10):2213-2222
In this paper, we provide a number of subdifferential formulas for a class of non-convex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time function. In particular, we generalize the results obtained recently by Zhang et al. 相似文献
16.
We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function into a once continuously differentiable function by way of the Moreau–Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. We prove the global convergence of the proposed method under the assumption of strong convexity of the objective function. 相似文献
17.
Satoshi Suzuki Daishi Kuroiwa 《Journal of Mathematical Analysis and Applications》2011,384(2):677-682
Recently, we discussed optimality conditions for quasiconvex programming by introducing ‘Q-subdifferential’, which is a notion of differential of quasiconvex functions. In this paper, we investigate basic and fundamental properties of the Q-subdifferential. Especially, we show results of a chain rule for composition with non-decreasing functions, monotonicity of the Q-subdifferential, mean-value theorem, a sufficient condition for a global minimizer for quasiconvex programming, and the calculus of the Q-subdifferential of the supremum of quasiconvex functions. 相似文献
18.
We investigate the scattering problem for a relativistic electron with spin in a Coulomb field in the framework of pseudoclassical mechanics. We obtain an analytic expression for the scattering angle and limiting estimates for the scattering parameters for the spinless and nonrelativistic cases. For small angles, the pseudoclassical model under consideration leads to the well-known quantum-mechanical Mott formula. 相似文献
19.
In this paper we examine a nonlinear elliptic problem driven by the p-Laplacian differential operator and with a potential function which is only locally Lipschitz, not necessarily C1 (hemivariational inequality). Using the nonsmooth critical point theory of Chang, we obtain two strictly positive solutions.
One solution is obtained by minimization of a suitable modification of the energy functional. The second solution is obtained
by generalizing a result of Brezis-Nirenberg about the local C10-minimizers versus the local H10-minimizers of a C1-functional.
Mathematics Subject Classification (2000) 35J50, 35J85, 35R70 相似文献
20.
Leszek Gasiński 《Journal of Mathematical Analysis and Applications》2002,276(2):723-746
In this paper we study a hyperbolic hemivariational inequality with a nonlinear, pseudomonotone operator depending on the derivative of an unknown function and a linear, monotone operator depending on an unknown function. Using the surjectivity result for L-pseudomonotone operators, an existence result for such inequalities is proved. 相似文献