Modified LS Method for Unconstrained Optimization

A Modified Regularized Newton Method for Unconstrained Nonconvex Optimization

In this paper, we present a modified regularized Newton method for the unconstrained nonconvex optimization by using trust region technique. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the modified regularized Newton method (M-RNM) has a global convergence property. Numerical results show that the algorithm is very efficient.

A Modified Conjugate Gradient Method for Unconstrained Optimization

Conjugate gradient methods are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been studied in depth. In this paper, we further study the conjugate gradient method for unconstrained optimization. We focus our attention to the descent conjugate gradient method. This paper presents a modified conjugate gradien...

The modified BFGS method with new secant relation ‎for unconstrained optimization problems‎

Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. U...

A Modified BFGS Algorithm for Unconstrained Optimization

In this paper we present a modified BFGS algorithm for unconstrained optimization. The BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi-Newton equation. The quasi-Newton condition can be interpreted as the interpolation condition that the gradient value of the local quadratic model matches that of the objective function at the previous iterate. Our modified al...

A modified secant method for unconstrained minimization