相关论文: A modified BFGS quasi-Newton iterative formula

In order to avoid the evaluation of the Jacobian matrix and its inverse, the present author recently introduced the pseudo-Jacobian matrix with a general applicability of any nonlinear systems of equations. By using this concept, this paper…

We investigate quasi-Newton methods for minimizing a strictly convex quadratic function which is subject to errors in the evaluation of the gradients. The methods all give identical behavior in exact arithmetic, generating minimizers of…

This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective…

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…

Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…

We consider the finite-sum optimization problem, where each component function is strongly convex and has Lipschitz continuous gradient and Hessian. The recently proposed incremental quasi-Newton method is based on BFGS update and achieves…

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined BFGS and L-BFGS updates in local and global coordinates…

We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…

We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also…

Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…

In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…

Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…

The classical convergence analysis of quasi-Newton methods assumes that the function and gradients employed at each iteration are exact. In this paper, we consider the case when there are (bounded) errors in both computations and establish…

In recent years, interface quasi-Newton methods have gained growing attention in the fluid-structure interaction community by significantly improving partitioned solution schemes: They not only help to control the inherent added-mass…

We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…

Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…

By using the Hadamard matrix product concept, this paper introduces two generalized matrix formulation forms of numerical analogue of nonlinear differential operators. The SJT matrix-vector product approach is found to be a simple,…

This paper proposes a novel stochastic version of damped and regularized BFGS method for addressing the above problems.

A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it…