相关论文: A Globally Convergent LCL Method for Nonlinear Opt…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…

Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…

First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved inexact ALM (iALM) and conduct a unified analysis for…

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…

This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with…

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…

We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural…

The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…

In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated…

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…