Related papers: Mapping NP-hard and NP-complete optimisation probl…

In this paper we investigate the workflow scheduling problem, a known NP-hard class of scheduling problems. We derive problem instances from an industrial use case and compare against several quantum, classical, and hybrid quantum-classical…

We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach…

It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but…

Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic…

We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…

We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…

Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…

We study the optimization version of the equal cardinality set partition problem (where the absolute difference between the equal sized partitions' sums are minimized). While this problem is NP-hard and requires exponential complexity to…

We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…

We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from an approximation to the Quantum Adiabatic Algorithm (QAA). In solving…

Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard combinatorial optimization problems in the form of binary variables. The Hamiltonian function is often used to formulate QUBO problems where…

To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…

Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware…

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…

Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…

We introduce a novel quadratic unconstrained binary optimization (QUBO) formulation for a classical problem in electrical engineering -- the optimal reconfiguration of distribution grids. For a given graph representing the grid…