We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

The multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations. We describe how this technique can be combined with a globally convergent approximate Newton method to solve nonlinear partial differential equations. We show that asymptotically only one Newton iteration per level is required; thus the comp...

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

Steady state analysis of a 3-φ SEIG is generally done through mathematical modeling of its equivalent circuit. The impedance model can be reduced in terms of two nonlinear simultaneous equations consisting of unspecified variables as magnetizing reactance Xm and generated frequency F. The steady state performance analysis of SEIG becomes uncomplicated once the values of Xm and F are explicitly ...

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...

A computational technique for unconstrained optimal control problems is presented. First an Euler discretization is carried out to obtain a finite-dimensional approximation of the continous-time (infinite-dimensional) problem. Then an inexact restoration (IR) method due to Birgin and Mart́ınez is applied to the discretized problem to find an approximate solution. Convergence of the technique to ...