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51.
Jean-Paul Penot Constantin Zalinescu 《Proceedings of the American Mathematical Society》2006,134(7):1937-1946
We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch-Brezis type.
52.
Jean-Paul Penot Constantin Z?linescu 《Journal of Mathematical Analysis and Applications》2008,347(1):188-203
Given a convergent sequence of Hamiltonians (Hn) and a convergent sequence of initial data (gn) for the first-order evolutionary Hamilton-Jacobi equation, we look for conditions ensuring that the sequences (un) and (vn) of Lax solutions and Hopf solutions respectively converge. The convergences we deal with are variational convergences. We take advantage of several recent results giving criteria for the continuity of usual operations. 相似文献
53.
We set up a formula for the Fréchet and ε-Fréchet subdifferentials of the difference of two convex functions. We even extend it to the difference of two approximately
starshaped functions. As a consequence of this formula, we give necessary and sufficient conditions for local optimality in
nonconvex optimization. Our analysis relies on the notion of gap continuity of multivalued maps and involves concepts of independent
interest such as the notions of blunt and sharp minimizers and the notion of equi-subdifferentiability.
相似文献
54.
Multipliers and Generalized Derivatives of Performance Functions 总被引:1,自引:0,他引:1
J.-P. Penot 《Journal of Optimization Theory and Applications》1997,93(3):609-618
It is known that multipliers in mathematical programming have to do with the interpretation of generalized derivatives for the performance function of some perturbed problem. In economics, this fact is known under the term of shadow price. Here, we point out a precise relationship with the subdifferential of the performance function in the contingent sense and in the Fréchet sense, which are the simplest notions of nonsmooth analysis. 相似文献
55.
We consider the question of integration of a multivalued operator T, that is the question of finding a function f such that Tf. If is the Fenchel–Moreau subdifferential, the above problem has been completely solved by Rockafellar, who introduced cyclic monotonicity as a necessary and sufficient condition. In this article we consider the case where f is quasiconvex and is the lower subdifferential <. This leads to the introduction of a property that is reminiscent to cyclic monotonicity. We also consider the question of the density of the domains of subdifferential operators. 相似文献
56.
Aris Daniilidis Pando Georgiev Jean-Paul Penot 《Transactions of the American Mathematical Society》2003,355(1):177-195
We introduce a notion of cyclic submonotonicity for multivalued operators from a Banach space to its dual. We show that if the Clarke subdifferential of a locally Lipschitz function is strictly submonotone on an open subset of , then it is also maximal cyclically submonotone on , and, conversely, that every maximal cyclically submonotone operator on is the Clarke subdifferential of a locally Lipschitz function, which is unique up to a constant if is connected. In finite dimensions these functions are exactly the lower C functions considered by Spingarn and Rockafellar.
57.
We encompass the Moreau-Yosida regularization process by infimal convolution into a general framework. This sheds light on the assumptions required for obtaining the usual properties. In particular the class of lower-T2 mappings is shown to be a suitable class for performing the usual proximal regularization in open subsets of Hilbert spaces. The role of growth conditions is pointed out. 相似文献
58.
Jean-Paul Penot Pham Hong Quang 《Journal of Optimization Theory and Applications》2011,148(3):455-470
A notion of boundedly ε-lower subdifferentiable functions is introduced and investigated. It is shown that a bounded from below, continuous, quasiconvex
function is locally boundedly ε-lower subdifferentiable for every ε>0. Some algorithms of cutting plane type are constructed to solve minimization problems with approximately lower subdifferentiable
objective and constraints. In those algorithms an approximate minimizer on a compact set is obtained in a finite number of
iterations provided some boundedness assumption be satisfied. 相似文献
59.
N.?T.?H.?LinhEmail author J.-P.?Penot 《Journal of Optimization Theory and Applications》2012,154(2):321-338
We study some classes of generalized affine functions, using a generalized differential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes. 相似文献
60.