Related papers: Quantum Hamiltonian Descent for Non-smooth Optimiz…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
We explore the potential for quantum speedups in convex optimization using discrete simulations of the Quantum Hamiltonian Descent (QHD) framework, as proposed by Leng et al., and establish the first rigorous query complexity bounds. We…
Stochastic Gradient Descent (SGD) and its variants underpin modern machine learning by enabling efficient optimization of large-scale models. However, their local search nature limits exploration in complex landscapes. In this paper, we…
We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to…
In this paper, we identify a family of nonconvex continuous optimization instances, each $d$-dimensional instance with $2^d$ local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently…
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…
Quantum Hamiltonian Descent (QHD) is a continuous optimization algorithm based on simulating a time-dependent quantum Hamiltonian whose potential energy encodes the objective function and whose kinetic energy promotes exploration through…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms.…
This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…
We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic…
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…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…