Related papers: An Exceptionally Difficult Binary Quadratic Optimi…
For the Lagrangian-DNN relaxation of quadratic optimization problems (QOPs), we propose a Newton-bracketing method to improve the performance of the bisection-projection method implemented in BBCPOP [to appear in ACM Tran. Softw., 2019].…
We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
Solving combinatorial optimization problems (COPs) is a promising application of quantum computation, with the Quantum Approximate Optimization Algorithm (QAOA) being one of the most studied quantum algorithms for solving them. However,…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…
Algorithms and hardware for solving quadratic unconstrained binary optimization (QUBO) problems have made significant recent progress. This advancement has focused attention on formulating combinatorial optimization problems as quadratic…
The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be…
Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is…
This paper proposes two approaches for inferencing binary codes in two-step (supervised, unsupervised) hashing. We first introduce an unified formulation for both supervised and unsupervised hashing. Then, we cast the learning of one bit as…
The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…
The aim of the paper is to propose a bounded-error quantum polynomial time (BQP) algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
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…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…
This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…