An accelerated directional derivative method for smooth stochastic convex optimization

P Dvurechensky, E Gorbunov, A Gasnikov - European Journal of …, 2021 - Elsevier
We consider smooth stochastic convex optimization problems in the context of algorithms
which are based on directional derivatives of the objective function. This context can be …

Existence theorems for elliptic and evolutionary variational and quasi-variational inequalities

AA Khan, D Motreanu - Journal of Optimization Theory and Applications, 2015 - Springer
This paper gives new existence results for elliptic and evolutionary variational and quasi-
variational inequalities. Specifically, we give an existence theorem for evolutionary …

Directional differentiability for elliptic quasi-variational inequalities of obstacle type

A Alphonse, M Hintermüller, CN Rautenberg - Calculus of Variations and …, 2019 - Springer
The directional differentiability of the solution map of obstacle type quasi-variational
inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical …

Fractional elliptic quasi-variational inequalities: theory and numerics

H Antil, CN Rautenberg - Interfaces and Free Boundaries, 2018 - ems.press
Fractional elliptic quasi-variational inequalities: Theory and numerics Page 1 Interfaces and
Free Boundaries 20 (2018), 1–24 DOI 10.4171/IFB/395 Fractional elliptic quasi-variational …

Stability of the solution set of quasi-variational inequalities and optimal control

A Alphonse, M Hintermüller, CN Rautenberg - SIAM Journal on Control and …, 2020 - SIAM
For a class of quasi-variational inequalities (QVIs) of obstacle type the stability of its solution
set and associated optimal control problems are considered. These optimal control …

A new class of evolution multivalued quasi-variational inequalities I: existence and nonsmooth optimal control

S Zeng, VD Rădulescu - ar** process
H Antil, R Arndt, BS Mordukhovich, D Nguyen… - arxiv preprint arxiv …, 2022 - arxiv.org
The paper addresses the study of a class of evolutionary quasi-variational inequalities of the
parabolic type arising in the formation and growth models of granular and cohensionless …

Nondiffusive variational problems with distributional and weak gradient constraints

H Antil, R Arndt, CN Rautenberg… - Advances in Nonlinear …, 2022 - degruyter.com
In this article, we consider nondiffusive variational problems with mixed boundary conditions
and (distributional and weak) gradient constraints. The upper bound in the constraint is …