we present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step q-superlinear convergence. the approach is based on an adaptive structured scheme due to mahdavi-amiri and bartels of the exact penalty method of coleman and conn for nonlinearly constrained optimization problems. the structured adaptation also makes use of the ideas of n...

We present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of N...

In this paper, we investigate a symmetric rank-one (SR1) quasi-Newton (QN) formula in which the Hessian of the objective function has some special structure. Instead of approximating the whole Hessian via the SR1 formula, we consider an approach which only approximates part of the Hessian matrix that is not easily acquired. Although the SR1 update possesses desirable features, it is unstable in...

We present an exact penalty approach for solving constrained nonlinear least squares problems, using a new projected structured Hessian approximation scheme. We establish general conditions for the local two-step Q-superlinear convergence of our given algorithm. The approach is general enough to include the projected version of the structured PSB, DFP and BFGS formulas as special cases. The num...

Numerical solution of nonlinear least-squares problems is an important computational task in science and engineering. Effective algorithms have been developed for solving nonlinear least squares problems. The structured secant method is a class of efficient methods developed in recent years for optimization problems in which the Hessian of the objective function has some special structure. A pr...

Recently, a derivative-free optimization algorithm was proposed that utilizes minimum Frobenius norm (MFN) Hessian update for estimating the second derivative information, which in turn is used accelerating search. The formula relies only on computed function values and closed-form expression special case of more general approach first published by Powell. This paper analyzes convergence under ...

The BFGS update and the DFP update perhaps are respectively the most successful Hessian and inverse Hessian approximations for unconstrained minimization problems This paper describes a geometric meaning of these updates understood from the Wedderburn rank one reduction formula

A Hessian matrix in full waveform inversion (FWI) is difficult to compute directly because of high computational cost and an especially large memory requirement. Therefore, Newton-like methods are rarely feasible in realistic largesize FWI problems. We modify the BFGS method to use a projected Hessian matrix that reduces both the computational cost and memory required, thereby making a quasiNew...