Related papers: Comparative analysis of mathematical formulations …
We consider an enhanced version of the well-kwown "Petrov-Galerkin" projection in Hilbert spaces. The proposed procedure, dubbed "multi-slice" projector, exploits the fact that the sought solution belongs to the intersection of several…
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…
Symmetry handling inequalities (SHIs) are a popular tool to handle symmetries in integer programming. Despite their successful application in practice, only little is known about the interaction of SHIs with optimization problems. In this…
Portfolio optimization is one of the most studied optimization problems at the intersection of quantum computing and finance. In this work, we develop the first quantum formulation for a portfolio optimization problem with higher-order…
This study investigates the area of general quadratic integer programming (QIP), encompassing both unconstrained (UQIP) and constrained (CQIP) variants. These NP-hard problems have far-reaching applications, yet the non-convex cases have…
We investigate the recoverable robust single machine scheduling problem under interval uncertainty. In this setting, jobs have first-stage processing times p and second-stage processing times q and we aim to find a first-stage and…
Variational quantum algorithms have been advocated as promising candidates to solve combinatorial optimization problems on near-term quantum computers. Their methodology involves transforming the optimization problem into a quadratic…
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
We seek shifted lattice rules that are good for high dimensional integration over the unit cube in the setting of an unanchored weighted Sobolev space of functions with square-integrable mixed first derivatives. Many existing studies rely…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
This paper addresses the complex issue of resource-constrained scheduling, an NP-hard problem that spans critical areas including chip design and high-performance computing. Traditional scheduling methods often stumble over scalability and…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
Two-stage stochastic mixed-integer linear programs with mixed-integer recourse arise in many practical applications but are computationally challenging due to their large size and the presence of integer decisions in both stages. The…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y'(x)=f(x,Y(x)) using matrix-cubic…
The p-median problem concerns the location of facilities so that the sum of distances between the demand points and their nearest facility is minimized. We study a variant of this classic location problem where minimum distance constraints…
Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…