相关论文: Analytical Gradient Theory for Resolvent-Fitted Se…

We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

We consider the class of disjoint bilinear programs $ \max \, \{ \mathbf{x}^T\mathbf{y} \mid \mathbf{x} \in \mathcal{X}, \;\mathbf{y} \in \mathcal{Y}\}$ where $\mathcal{X}$ and $\mathcal{Y}$ are packing polytopes. We present an…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Policy gradient methods are a powerful family of reinforcement learning algorithms for continuous control that optimize a policy directly. However, standard first-order methods often converge slowly. Second-order methods can accelerate…

We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…

This article presents an alternative formulation of quasi-degenerate perturbation theory (QDPT). The development results by simplifying established many-body (MB) techniques to systems of non-interacting particles (NIP). While the physical…

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs…

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…