Related papers: Quantum Hamiltonian Descent for Non-smooth Optimiz…
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…
Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…
Generalized and Simulated Method of Moments are often used to estimate structural Economic models. Yet, it is commonly reported that optimization is challenging because the corresponding objective function is non-convex. For smooth…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
We present a quantum-inspired algorithm that utilizes Quantum Hamiltonian Descent (QHD) for efficient community detection. Our approach reformulates the community detection task as a Quadratic Unconstrained Binary Optimization (QUBO)…