Related papers: A Differentiable Augmented Lagrangian Method for B…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
The multi-contact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in…
Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…
In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…
We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented…
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a…
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…
This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…