Related papers: A Unified and Scalable Method for Optimization ove…
Process Planning and Scheduling (PPS) is an essential and practical topic but a very intractable problem in manufacturing systems. Many research use iterative methods to solve such problems; however, they cannot achieve satisfactory results…
We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models. An edge sampling scheme is used to build a low-complexity problem that is used to finding an approximate (but…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
We study a natural extension of the Maximum Weight Independent Set Problem (MWIS), one of the most studied optimization problems in Graph algorithms. We are given a graph $G=(V,E)$, a weight function $w: V \rightarrow \mathbb{R^+}$, a…
Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…
The network embedding problem that maps nodes in a graph to vectors in Euclidean space can be very useful for addressing several important tasks on a graph. Recently, graph neural networks (GNNs) have been proposed for solving such a…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph G = (V,A) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
The rapid growth of graph data poses significant challenges in storage, transmission, and particularly the training of graph neural networks (GNNs). To address these challenges, graph condensation (GC) has emerged as an innovative solution.…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…