Improved Hessian approximation with modified secant equations for symmetric rank-one method

Improved Hessian approximation with modified secant equations for symmetric rank-one method

Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new a...

Hessian Equations with Elementary Symmetric Functions

We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the C space are provided.

A Rank-One Fitting Method with Descent Direction for Solving Symmetric Nonlinear Equations

In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: 1) The updated matrix is positive definite whatever line search technique is used; 2) The search direction is descent for the norm function; 3) The global convergence of the given method is established under reasonable conditions. Numerical results show that the p...

Memoryless Modified Symmetric Rank-One Method for Large-Scale Unconstrained Optimization

Problem statement: Memoryless QN methods have been regarded effective techniques for solving large-scale problems that can be considered as one step limited memory QN methods. In this study, we present a scaled memoryless modified Symmetric Rank-One (SR1) algorithm and investigate the numerical performance of the proposed algorithm for solving large-scale unconstrained optimization problems. Ap...

A modified secant method for unconstrained minimization