Related papers: Lagrangian Relaxation for MAP Estimation in Graphi…

Linear programming relaxations are central to {\sc map} inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using…

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…

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…

Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…

We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…

Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel…

We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…

This work introduces an unconventional inexact augmented Lagrangian method where the augmenting term is a Euclidean norm raised to a power between one and two. The proposed algorithm is applicable to a broad class of constrained nonconvex…

In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…

Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…

Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…

In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle…

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…