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We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
This paper describes Nancy, a Network Calculus (NC) library that allows users to perform complex min-plus and max-plus algebra operations efficiently. To the best of our knowledge, Nancy is the only open-source library that implements…
Many emerging commercial services are based on the sharing or pooling of resources for common use with the aim of reducing costs. Businesses such as delivery-, mobility-, or transport-as-a-service have become standard in many parts of the…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…
Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the…
A lot of problems, from fields like sparse signal processing, statistics, portfolio selection, and machine learning, can be formulated as a cardinality constraint optimization problem. The cardinality constraint gives the problem a discrete…
Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial…
Processing large Pauli sums is a significant bottleneck in quantum chemistry, Pauli propagation, and Pauli-based compilation. Existing frameworks often suffer from Python interpreter overhead or utilize hash-map data structures that hinder…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
The lattice Boltzmann method (LBM) has emerged as a prominent technique for solving fluid dynamics problems due to its algorithmic potential for computational scalability. We introduce XLB library, a Python-based differentiable LBM library…
Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…