相关论文: On the Exactness of Dantzig-Wolfe Relaxation for R…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization…

The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model multi-agent coordination problems that are distributed by nature. The formulation is suitable for problems where variables are discrete and…

We study a resource-constrained variant of the Random Disambiguation Path (RDP) problem, a generalization of the Stochastic Obstacle Scene (SOS) problem, in which a navigating agent must reach a target in a spatial environment populated…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as…

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…

This paper presents a model-free reinforcement learning (RL) algorithm to solve the risk-averse optimal control (RAOC) problem for discrete-time nonlinear systems. While successful RL algorithms have been presented to learn optimal control…

This paper is concerned with the Frank--Wolfe algorithm for a special class of {\it non-compact} constrained optimization problems. The notion of asymptotic cone is used to introduce this class of problems as well as to establish that the…

In this paper, we concentrate on a particular category of quadratically constrained quadratic programming (QCQP): nonconvex QCQP with one equality constraint. This type of QCQP problem optimizes a quadratic objective under a fixed…

We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…

A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…

Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…

In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnegative vector as variables. We develop a rank-support-adaptive…

Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the convex formulation is commonly replaced by…

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and…

The discrete unit commitment problem with min-stop ramping constraints optimizes the daily production of thermal power plants (coal, gas, fuel units). For this problem, compact Integer Linear Programming (ILP) formulations have been…