Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

Superlinearly convergent exact penalty projected structured Hessian updating schemes for constrained nonlinear least squares: asymptotic analysis

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...

A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...

Two new three and four parametric with memory methods for solving nonlinear ‎equations

In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

Derivative-Free Optimization for Parameter Estimation in Computational Nuclear Physics

We consider optimization problems that arise when estimating a set of unknown parameters from experimental data, particularly in the context of nuclear density functional theory. We examine the cost of not having derivatives of these functionals with respect to the parameters. We show that the POUNDERS code for local derivative-free optimization obtains consistent solutions on a variety of comp...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations