10 papers
Dynamic Proximal Point Method for Unconstrained Minimization
Enrico Bertolazzi, Alberto De Marchi, Davide Stocco
In this work, we present a novel dynamic proximal point algorithm for unconstrained optimization. The method generates a sequence of proximal subproblems, where the quadratic regul…
Elastically safeguarded augmented Lagrangian methods
Ernesto G. Birgin, Alberto De Marchi, Patrick Mehlitz
We investigate, theoretically and numerically, a class of elastically safeguarded augmented Lagrangian methods for nonlinear optimization problems with inequality and equality cons…
Augmented Lagrangian methods for fully convex composite optimization
Alberto De Marchi, Tim Hoheisel, Patrick Mehlitz
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented…
Resolvent Moreau identities without monotonicity: theory and applications to Gabay duality, Douglas--Rachford and ADMM
Andrew Calcan, Jordan Collard, Alberto De Marchi +1
Duality is most often defined as a relationship between convex functions. If those functions are nonconvex, classical duality breaks down. Notwithstanding, we show that another kin…
Reinforcement learning for adaptive interior point methods in convex quadratic programming
Jeremy Bertoncini, Alberto De Marchi, Matthias Gerdts +1
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumption…
Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization
Simeon vom Dahl, Alberto De Marchi, Christian Kanzow
We introduce a proximal limited--memory quasi--Newton scheme for minimizing the sum of a continuously differentiable function and a proper, lower semicontinuous and prox-bounded, p…