arXiv subjects

Robert Benkoczi

Publications and source records attributed to Robert Benkoczi.

5 recordsLinked to original sources

arXiv2024

Quantum Algorithms for Optimal Power Flow

This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to classical methods. The simulation results presented here which substantially improve the results in [1] indicate that quantum approaches yield similar solutions and optimal costs compared to classical methods, suggesting the potential use case of quantum computing for power system optimization.

quant-ph↗

arXiv2024

A hybrid quantum solver for the Lorenz system

We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational Quantum Linear Solver (VQLS) algorithm. We present numerical results comparing the hybrid method with the classical approach for solving the Lorenz system. The simulation results demonstrate that the VQLS method can effectively compute solutions comparable to classical methods. The method is easily extended to solving similar nonlinear differential equations.

quant-ph↗

arXiv2024

A Hybrid Quantum Algorithm for Load Flow

The goal of the load flow study is to ensure that electrical power is delivered efficiently and reliably to end-users while maintaining the stability and security of the power system. Newton-Raphson is a numerical method used widely for load flow analysis. One of the most computationally expensive steps in this method is an equation-solving step. We propose to replace this step with HHL, a quantum algorithm for solving linear systems of equations. HHL is exponentially faster, but with caveats. In this study, a hybrid quantum algorithm is proposed for solving load flow. The Newton-Raphson method is used as a benchmark to compare the performance of the hybrid quantum algorithm. Although the simulation of the hybrid quantum algorithm takes much time, these preliminary results are encouraging and point to the potential for the use of quantum algorithms to develop hybrid quantum algorithms for load flow analysis and related problems.

eess.SY↗

arXiv2021

Barzilai and Borwein conjugate gradient method equipped with a non-monotone line search technique and its application on non-negative matrix factorization

In this paper, we propose a new non-monotone conjugate gradient method for solving unconstrained nonlinear optimization problems. We first modify the non-monotone line search method by introducing a new trigonometric function to calculate the non-monotone parameter, which plays an essential role in the algorithm's efficiency. Then, we apply a convex combination of the Barzilai-Borwein method for calculating the value of step size in each iteration. Under some suitable assumptions, we prove that the new algorithm has the global convergence property. The efficiency and effectiveness of the proposed method are determined in practice by applying the algorithm to some standard test problems and non-negative matrix factorization problems.

math.OC↗

arXiv2018

Minsum $k$-Sink Problem on Path Networks

We consider the problem of locating a set of $k$ sinks on a path network with general edge capacities that minimizes the sum of the evacuation times of all evacuees. We first present an $O(kn\log^4n)$ time algorithm when the edge capacities are non-uniform, where $n$ is the number of vertices. We then present an $O(kn\log^3 n)$ time algorithm when the edge capacities are uniform. We also present an $O(n\log n)$ time algorithm for the special case where $k=1$ and the edge capacities are non-uniform.

cs.DS↗