4 papers
Optimal design with uncertainties: a risk-averse approach
Amal Alphonse, Petar Kunštek, Marko Vrdoljak
We study a class of stochastic optimal design problems for elliptic partial differential equations in divergence form, where the coefficients represent mixtures of two conducting m…
Skip the Hessian, Keep the Rates: Globalized Semismooth Newton with Lazy Hessian Updates
Amal Alphonse, Pavel Dvurechensky, Clemens Sirotenko
Second-order methods are provably faster than first-order methods, and their efficient implementations for large-scale optimization problems have attracted significant attention. Y…
LeAP-SSN: A Semismooth Newton Method with Global Convergence Rates
Amal Alphonse, Pavel Dvurechensky, Ioannis P. A. Papadopoulos +1
We propose LeAP-SSN (Levenberg--Marquardt Adaptive Proximal Semismooth Newton method), a semismooth Newton-type method with a simple, parameter-free globalisation strategy that gua…
Subdifferentials and penalty approximations of the obstacle problem
Amal Alphonse, Gerd Wachsmuth
We consider a framework for approximating the obstacle problem through a penalty approach by nonlinear PDEs. By using tools from capacity theory, we show that derivatives of the so…