Related papers: Non-convex Quadratic Programming Using Coherent Op…
This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems: max-cut, number partitioning, knapsack, and quantum spin glass. Our benchmark includes noisy…
We introduce the Suggest-and-Improve framework for general nonconvex quadratically constrained quadratic programs (QCQPs). Using this framework, we generalize a number of known methods and provide heuristics to get approximate solutions to…
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
Quantum computing is among the most promising emerging techniques to solve problems that are computationally intractable on classical hardware. A large body of existing works focus on using variational quantum algorithms on the gate level…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…
In this paper we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems. These computers, at least in principle, can be realized by actually existing devices. We estimate…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…
We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…