Accelerated derivative-free spectral residual method for nonlinear systems of equations

Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely … Read more

Error estimates for the Euler discretization of an optimal control problem with first-order state constraints

We study the error introduced in the solution of an optimal control problem with first order state constraints, for which the trajectories are approximated with a classical Euler scheme. We obtain order one approximation results in the $L^\infty$ norm (as opposed to the order 2/3 obtained in the literature). We assume either a strong second … Read more

Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and … Read more

New Versions of Interior Point Methods Applied to the Optimal Power Flow Problem

Interior Point methods for Nonlinear Programming have been extensively used to solve the Optimal Power Flow problem. These optimization algorithms require the solution of a set of nonlinear equations to obtain the optimal solution of the power network equations. During the iterative process to solve these equations, the search for the optimum is based on … Read more