Related papers: A practical framework for infinite-dimensional lin…
This paper proposes a quasi-binary encoding based algorithm for solving a specific quadratic optimization models with discrete variables, in the quantum approximate optimization algorithm (QAOA) framework. The quadratic optimization model…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and…
We introduce a quantum linear system solving algorithm based on the Kaczmarz method, a widely used workhorse for large linear systems and least-squares problems that updates the solution by enforcing one equation at a time. Its simplicity…
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…
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…
Combinatorial optimization lies at the heart of numerous real-world applications. For a broad category of optimization problems, quantum computing is expected to exhibit quantum speed-up over classic computing. Among various quantum…
Continuous-variable (CV) quantum systems offer a natural framework for continuous optimization through their infinite-dimensional Hilbert spaces. In this paper, we propose the Complex Continuous-Variable Quantum Approximate Optimization…
We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the…
While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for finite dimensional systems. We show that this result extends…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…