Solving Nonlinear Systems of Equations With Simple Constraints

A general algorithm for solving F (x) = 0, x 2 \Omega\Gamma where F : IR n ! IR n is a differentiable function and\Omega is closed and convex, is introduced. The new method uses the inexact-Newton approach with a globalization procedure. Conditions are given that ensure global convergence to a solution of the problem. Numerical experiments where \Omega is an n\Gammadimensional box are presented. Keywords. Nonlinear systems, inexact - Newton method, global convergence, convex constraints, box constraints. AMS: 65H10 Department of Mathematics, Federal University of Santa Catarina, Florian'opolis, Santa Catarina, Brazil. This author was supported by FAPESP (Grant 90-3724-6). y Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil ([email protected]). This author was supported by FAPESP (Grant 90-3724-6), CNPq, FINEP and FAEP-UNICAMP. z Department of Mathematics, IMECC-UNICAMP, University of Campinas, CP 6..

A Numerical Study on Large-Scale Nonlinear Solvers

We consider the solution of several nonlinear systems that come from the discretization of two-dimensional boundary value problems using well-known algorithms based on the quasi-Newton idea: Newton 's method, Broyden's method and the Column-Updating method. Numerical results can be useful for researchers to indicate the performances that should be improved by future algorithms or implementations. Key words. Nonlinear systems, quasi-Newton methods, Newton's method, globalization. 1 Introduction In this numerical study, we compare Newton and quasi-Newton methods using a simple globalization strategy, based on monotone decrease of the Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil ([email protected]). This work was supported by FAPESP (Grant 90-3724-6), FINEP and FAEP-UNICAMP. Present address of D. N. Kozakevich: Departmento of Mathematics, Federal University of Santa Catarina, Florian'opolis, Santa Catarina, Braz..