相关论文: On Convergence of Regularized Barzilai-Borwein Met…
Due to simplicity, computational cheapness, and efficiency, the Barzilai and Borwein (BB) gradient method has received a significant amount of attention in different fields of optimization. In the first part of this paper, based on spectral…
The Barzilai-Borwein (BB) method has demonstrated great empirical success in nonlinear optimization. However, the convergence speed of BB method is not well understood, as the known convergence rate of BB method for quadratic problems is…
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize is the close solution to a $\ell_{2}^{2}$-regularized least…
The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In…
The Barzilai-Borwein (BB) method is an effective gradient descent algorithm for solving unconstrained optimization problems. Based on the observation of two classical BB step sizes, by constructing an interpolated least squares model, we…
The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different.…
We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton…
The Barzilai-Borwein (BB) step sizes have a profound impact on gradient descent methods. In this work, we propose two new gradient step sizes: one longer than the original long BB step size, and the other shorter than the original short BB…
In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for…
A novel gradient stepsize is derived at the motivation of equipping the Barzilai-Borwein (BB) method with two dimensional quadratic termination property. A remarkable feature of the novel stepsize is that its computation only depends on the…
In this paper, we consider to improve the stochastic variance reduce gradient (SVRG) method via incorporating the curvature information of the objective function. We propose to reduce the variance of stochastic gradients using the…
One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms,…
When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the…
We consider a distributed multi-agent optimization problem over a time-invariant undirected graph, where each agent possesses a local objective function and all agents collaboratively minimize the average of all objective functions through…
The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein "two-point step size" strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the…
Variable metric proximal gradient methods with different metric selections have been widely used in composite optimization. Combining the Barzilai-Borwein (BB) method with a diagonal selection strategy for the metric, the diagonal BB…
StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating…
Variable metric proximal gradient (VM-PG) is a widely used class of convex optimization method. Lately, there has been a lot of research on the theoretical guarantees of VM-PG with different metric selections. However, most such metric…
The growth in sizes of large-scale systems and data in machine learning have made distributed optimization a naturally appealing technique to solve decision problems in different contexts. In such methods, each agent iteratively carries out…
Recent studies show that the two-dimensional quadratic termination property has great potential in improving performance of the gradient method. However, it is not clear whether higher-dimensional quadratic termination leads further…