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1.
Lionel Thibault Nadia Zlateva 《Proceedings of the American Mathematical Society》2005,133(10):2939-2948
Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.
2.
Giovanni Cupini Marcello Guidorzi Cristina Marcelli 《Journal of Differential Equations》2007,243(2):329-348
Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained. 相似文献
3.
梅家骝 《高校应用数学学报(A辑)》1989,4(4):541-549
本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。 相似文献
4.
《Optimization》2012,61(1-2):35-110
We endeavour to answer the question of the title, or rather the question of how much one can extend convex analysis to a wider framework in which some convexity features remain. Subdifferential calculus and duality are the main directions we consider 相似文献
5.
《Set-Valued Analysis》2008,16(2-3):199-227
The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between
finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative
criterion for “full” metric regularity but involves a different type of coderivative which is introduced in the paper. We
also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic
calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in
terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly
associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich–Rockafellar
subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and,
more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show,
for each of the calculus rules, that the standard qualification conditions are equivalent to “full” metric regularity of precisely
the same mappings that are involved in the subregularity version of our calmness/subregularity condition.
The research of Jiří V. Outrata was supported by the grant A 107 5402 of the Grant Agency of the Academy of Sciences of the
Czech Republic. 相似文献
6.
Hédy Attouch Guillaume Garrigos Xavier Goudou 《Journal of Mathematical Analysis and Applications》2015
In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving nonsmooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the objective functions, a key property for applications in cooperative games, inverse problems, and numerical multiobjective optimization. 相似文献
7.
Stanis?aw Migórski Anna Ochal 《Journal of Mathematical Analysis and Applications》2005,306(1):197-217
In this paper we study a class of inequality problems for the stationary Navier-Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier-Stokes ones for the velocity and pressure with nonstandard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps. We also establish a result on the dependence of the solution set with respect to a locally Lipschitz superpotential appearing in the boundary condition. 相似文献
8.
S. Simons 《Journal of Optimization Theory and Applications》1991,71(1):127-136
In this paper, we give a direct proof of Rockafellar's result that the subdifferential of a proper convex lower-semicontinuous function on a Banach space is maximal monotone. Our proof is simpler than those that have appeared to date. In fact, we show that Rockafellar's result can be embedded in a more general situation in which we can quantify the degree of failure of monotonicity in terms of a quotient like the one that appears in the definition of Fréchet differentiability. Our analysis depends on the concepts of the least slope of a convex function, which is related to the steepest descent of optimization theory.The author would like to express his thanks to R. R. Phelps for reading a preliminary version of this paper and making some very valuable suggestions. 相似文献
9.
本文研究了Banach空间上凸函数项级数,给出了Moreau Rockafelar定理的推广,做为它的应用,获得了Kuhn Tucker定理的一个部分推广. 相似文献
10.
Gonzalo Alduncin 《Numerical Functional Analysis & Optimization》2013,34(7-8):751-774
In the context of convex analysis, macro-hybrid variational formulations of constrained boundary value problems are presented. Monotone mixed variational inclusions are macro-hybridized on the basis of nonoverlapping domain decompositions, and corresponding three-field versions are derived. Then, for regularization purposes, augmented formulations are established via preconditioned exact penalizations and expressed in terms of proximation operators. Optimization interpretations are given for potential problems, recovering the classic two- and three-field augmented Lagrangian formulations. Furthermore, associated parallel two- and three-field proximal-point algorithms are discussed for numerical resolution of finite element discretizations. Applications to dual mixed variational formulations of problems from mechanics illustrate the theory. 相似文献