Related papers: A Unified and Scalable Method for Optimization ove…
In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane…
This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes…
Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such…
We consider the problem of matrix completion with graphs as side information depicting the interrelations between variables. The key challenge lies in leveraging the similarity structure of the graph to enhance matrix recovery. Existing…
In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex…
We address the Multi-Robot Motion Planning (MRMP) problem of computing collision-free trajectories for multiple robots in shared continuous environments. While existing frameworks effectively decompose MRMP into single-robot subproblems,…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets…
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
Given an undirected node-weighted graph, the Maximum-Weight Connected Subgraph problem (MWCS) is to identify a subset of nodes of maximalsum of weights that induce a connected subgraph. MWCS is closely related to the well-studied Prize…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…
In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical…