54 research outputs found
Stability analysis of partial differential variational inequalities in Banach spaces
In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques
Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming
This paper concerns parameterized convex infinite (or semi-infinite)
inequality systems whose decision variables run over general
infinite-dimensional Banach (resp. finite-dimensional) spaces and that are
indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand
side of the inequalities are measurable and bounded, and thus the natural
parameter space is . Based on advanced variational analysis, we
derive a precise formula for computing the exact Lipschitzian bound of the
feasible solution map, which involves only the system data, and then show that
this exact bound agrees with the coderivative norm of the aforementioned
mapping. On one hand, in this way we extend to the convex setting the results
of [4] developed in the linear framework under the boundedness assumption on
the system coefficients. On the other hand, in the case when the decision space
is reflexive, we succeed to remove this boundedness assumption in the general
convex case, establishing therefore results new even for linear infinite and
semi-infinite systems. The last part of the paper provides verifiable necessary
optimality conditions for infinite and semi-infinite programs with convex
inequality constraints and general nonsmooth and nonconvex objectives. In this
way we extend the corresponding results of [5] obtained for programs with
linear infinite inequality constraints
On a sub-supersolution method for the prescribed mean curvature problem
summary:The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established
Metric Regularity of the Sum of Multifunctions and Applications
In this work, we use the theory of error bounds to study metric regularity of
the sum of two multifunctions, as well as some important properties of
variational systems. We use an approach based on the metric regularity of
epigraphical multifunctions. Our results subsume some recent results by Durea
and Strugariu.Comment: Submitted to JOTA 37 page
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