Filter-type Algorithms for Solving Systems of Algebraic Equations and Inequalities

Abstract

The problem of solving a nonlinear system is transformed into a bi-objective nonlinear programming problem, which is then solved by a prototypical trust region filter SQP algorithm. The definition of the bi-objective problems is changed adaptively as the algorithm proceeds. The method permits the use of second order information and hence enables rapid local convergence to occur, which is particularly important for solving locally infeasible problems. A proof of global convergence is presented under mild assumptions.