14 papers · 1 filter
Interior-point proximal methods for nonsmooth optimization in Hilbert spaces with cone-ordered constraints
Behzad Azmi, Alberto De Marchi
We study an inexact interior-point method for nonsmooth, nonconvex optimization problems with conic inequality constraints. The objective function is given by the sum of a smooth,…
Mirror descent algorithms with logarithmic barriers
Alberto De Marchi, Yura Malitsky, Adrien B. Taylor
This work derives convergence guarantees for mirror descent and proximal mirror descent algorithms when a logarithmic barrier is used as a distance-generating function. Standard ap…
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…
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…
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…