Related papers: Graph-structured tensor optimization for nonlinear…
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…
Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches…
We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…
We study an optimal transport problem in a compact convex set $\Omega\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $\Omega$.…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. This is also known as convex/convergent…
We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an…
Recent years have witnessed the promise that reinforcement learning, coupled with Graph Neural Network (GNN) architectures, could learn to solve hard combinatorial optimization problems: given raw input data and an evaluator to guide the…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method…
This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…