30 citations · 98 across the 19 of their papers we have counts for
21 papers
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, possibly nonconvex optimization in a Hilbert space with inequality constraints ordered by a cone in a Banach lattice, with…
Envelopt: Constrained Convex Composite Optimization
Alberto De Marchi, Dominique Orban
We introduce Envelopt, a globally convergent iterative framework for a broad class of structured optimization problems where a smooth objective is augmented by a nonsmooth convex r…
Mirror descent algorithms with logarithmic barriers
Alberto De Marchi, Yura Malitsky, Adrien B. Taylor
We derive convergence guarantees for mirror descent and proximal mirror descent with a logarithmic barrier as the distance-generating function. When the solution lies on the bounda…
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 propose a regularized proximal quasi-Newton method (RPQN) for minimizing the sum of a continuously differentiable, possibly nonconvex function and a proper, lower semicontinuous…
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…
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…
Affordable mixed-integer Lagrangian methods: optimality conditions and convergence analysis
Alberto De Marchi
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions…
A penalty barrier framework for nonconvex constrained optimization
Alberto De Marchi, Andreas Themelis
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of…
Hybrid optimal control with mixed-integer Lagrangian methods
Viktoriya Nikitina, Alberto De Marchi, Matthias Gerdts
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with…
Collision Avoidance using Iterative Dynamic and Nonlinear Programming with Adaptive Grid Refinements
Rebecca Richter, Alberto De Marchi, Matthias Gerdts
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods stru…
Mixed-integer linearity in nonlinear optimization: a trust region approach
Alberto De Marchi
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a me…
Local properties and augmented Lagrangians in fully nonconvex composite optimization
Alberto De Marchi, Patrick Mehlitz
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentia…
Implicit augmented Lagrangian and generalized optimization
Alberto De Marchi
Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and s…
Relativistic Digital Twin: Bringing the IoT to the Future
Luca Sciullo, Alberto De Marchi, Angelo Trotta +3
Complex IoT ecosystems often require the usage of Digital Twins (DTs) of their physical assets in order to perform predictive analytics and simulate what-if scenarios. DTs are able…
Proximal gradient methods beyond monotony
Alberto De Marchi
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical…
An interior proximal gradient method for nonconvex optimization
Alberto De Marchi, Andreas Themelis
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schem…
Constrained composite optimization and augmented Lagrangian methods
Alberto De Marchi, Xiaoxi Jia, Christian Kanzow +1
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet s…
Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC
Alberto De Marchi, Andreas Themelis
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consid…