Related papers: A preconditioned augmented Lagrangian method for s…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…
Safety is a primary challenge in real-world reinforcement learning (RL). Formulating safety requirements as state-wise constraints has become a prominent paradigm. Handling state-wise constraints with the Lagrangian method requires a…
Constrained optimization is a powerful framework for enforcing requirements on neural networks. These constrained deep learning problems are typically solved using first-order methods on their min-max Lagrangian formulation, but such…
We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood.…
To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
We propose an efficient first-order method, based on the alternating direction method of multipliers (ADMM), to solve the homogeneous self-dual embedding problem for a primal-dual pair of semidefinite programs (SDPs) with chordal sparsity.…
In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\ell_1$ unit ball (QPL1). It dominates the state-of-the-art…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
We present preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from finite element discretizations of the fictitious domain method with Lagrange multipliers. In…
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…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
Square-root Lasso problems are proven robust regression problems. Furthermore, square-root regression problems with structured sparsity also plays an important role in statistics and machine learning. In this paper, we focus on the…
Within the framework of the augmented Lagrangian (AL), we propose a novel distributed optimization method, termed Distributed Augmented Lagrangian Decomposition (DALD), and provide a rigorous convergence proof for its standard version. To…
Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an…
In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for…
In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and…