Related papers: Family Column Generation: A Principled Stabilized …
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…
Clustering is a fundamental tool that has garnered significant interest across a wide range of applications including text analysis. To improve clustering accuracy, many researchers have incorporated background knowledge, typically in the…
We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…
Matrix factorization (MF) has been widely used in e.g., recommender systems, topic modeling and word embedding. Stochastic gradient descent (SGD) is popular in solving MF problems because it can deal with large data sets and is easy to do…
The recently introduced Genetic Column Generation (GenCol) algorithm has been numerically observed to efficiently and accurately compute high-dimensional optimal transport plans for general multi-marginal problems, but theoretical results…
The problem of column subset selection asks for a subset of columns from an input matrix such that the matrix can be reconstructed as accurately as possible within the span of the selected columns. A natural extension is to consider a…
Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…
Text embedding and generative tasks are usually trained separately based on large language models (LLMs) nowadays. This causes a large amount of training cost and deployment effort. Context compression is also a challenging and pressing…
In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated…
In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…
One of the major applications of generative models for drug Discovery targets the lead-optimization phase. During the optimization of a lead series, it is common to have scaffold constraints imposed on the structure of the molecules…
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
This article presents a novel approach to solving the sparsity-constrained Orthogonal Nonnegative Matrix Factorization (SCONMF) problem, which requires decomposing a non-negative data matrix into the product of two lower-rank non-negative…
A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…