4 citations · 8 across the 8 of their papers we have counts for
11 papers
A free boundary problem driven by boundary distance in the coincidence set
Amal Alphonse, Marcelo Bongarti, Enrico Valdinoci
We study a free boundary problem of minimising a functional containing a non-local term rewarding depth into the zero phase: for on a bounded, open set $Ω\subset\mat…
A neural network approach to learning solutions of a class of elliptic variational inequalities
Amal Alphonse, Michael Hintermüller, Alexander Kister +2
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the…
A Globalized Inexact Semismooth Newton Method for Nonsmooth Fixed-point Equations involving Variational Inequalities
Amal Alphonse, Constantin Christof, Michael Hintermüller +1
We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the fiel…
Minimal and maximal solution maps of elliptic QVIs of obstacle type: Lipschitz stability, differentiability and optimal control
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg +1
Quasi-variational inequalities (QVIs) of obstacle type in many cases have multiple solutions that can be ordered. We study a multitude of properties of the operator mapping the sou…
Risk-averse optimal control of random elliptic variational inequalities
Amal Alphonse, Caroline Geiersbach, Michael Hintermüller +1
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a pen…
On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
In this note, we prove that the minimal and maximal solution maps associated to elliptic quasi-variational inequalities of obstacle type are directionally differentiable with respe…
Optimal control and directional differentiability for elliptic quasi-variational inequalities
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal c…
Analysis of a quasi-variational contact problem arising in thermoelasticity
Amal Alphonse, Carlos N. Rautenberg, José Francisco Rodrigues
We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling…
Existence, iteration procedures and directional differentiability for parabolic QVIs
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs b…
Stability of the solution set of quasi-variational inequalities and optimal control
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
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 contro…
Directional differentiability for elliptic quasi-variational inequalities of obstacle type
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
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 class…