Related papers: Optimal Scaling Quantum Interior Point Method for …

Quantum interior point methods (QIPMs) promise polynomial speed-ups over classical solvers for linear programming by outsourcing the solution of Newton linear systems to quantum linear solvers (QLSAs). However, asymptotic speed-ups do not…

The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…

The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a…

We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional…

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…

Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…

Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…

Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of these solvers depends critically on the…

Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem…

Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…

Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…