相关论文: Projected gradient descent accumulates at Bouligan…

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the…

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

This paper presents an extension of stochastic gradient descent for the minimization of Lipschitz continuous loss functions. Our motivation is for use in non-smooth non-convex stochastic optimization problems, which are frequently…

Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…

There introduce Particle Optimized Gradient Descent (POGD), an algorithm based on the gradient descent but integrates the particle swarm optimization (PSO) principle to achieve the iteration. From the experiments, this algorithm has…

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection…

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal…

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and…

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with…

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization…

In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds. The generalized subdifferentials on Riemannian manifold and the Riemannian gradient sub-consistency…

We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient over the real determinantal variety, and present a first-order algorithm designed to find stationary points of that problem. This…

Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…

In this paper we propose and analyze a novel multilevel version of Stein variational gradient descent (SVGD). SVGD is a recent particle based variational inference method. For Bayesian inverse problems with computationally expensive…