Related papers: Learning based convex approximation for constraine…
Conventional solvers are often computationally expensive for constrained optimization, particularly in large-scale and time-critical problems. While this leads to a growing interest in using neural networks (NNs) as fast optimal solution…
Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi…
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…
Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…
Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…
In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…