相关论文: Mapping NP-hard and NP-complete optimisation probl…
Hypergraph partitioning is a fundamental optimization problem with applications in data management and other domains involving higher-order relations. In this paper, we study balanced hypergraph partitioning from the perspective of quantum…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation.…
Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
We consider sensitivity analysis for Mixed Binary Quadratic Programs (MBQPs) with respect to changing right-hand-sides (rhs). We show that even if the optimal solution of a given MBQP is known, it is NP-hard to approximate the change in…
We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse…
Quantum computing is developing fast. Real world applications are within reach in the coming years. One of the most promising areas is combinatorial optimisation, where the Quadratic Unconstrained Binary Optimisation (QUBO) problem…
This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
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…
Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various applications and are known to be NP-hard. The seminal work of Goemans and Williamson introduced a semidefinite programming (SDP) relaxation for such…
Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor…
The routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant maximum number of…
Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly…
We prove that the Max-Cut and Max-Bisection problems are NP-hard on unit disk graphs. We also show that $\lambda$-precision graphs are planar for $\lambda$ > 1 / \sqrt{2}$.
A challenge for scalability of demand-responsive, elastic optical Dense Wavelength Division Multiplexing (DWDM) and Flexgrid networks is the computational complexity of allocating many optical routes on large networks. We demonstrate that…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…