Conjugate Gradient Algorithms in the Solution of Optimization Problems for Nonlinear Elliptic Partial Differential Equations

TitleConjugate Gradient Algorithms in the Solution of Optimization Problems for Nonlinear Elliptic Partial Differential Equations
Publication TypeJournal Articles
Year of Publication1979
AuthorsO'Leary DP
JournalComputing
Volume22
Pagination59 - 77
Date Published1979///
Abstract

Several variants of the conjugate gradient algorithm are discussed with emphasis on determining the parameters without performing line searches and on using splitting techniques to accelerate convergence. The splittings used here are related to the nonlinear SSOR algorithm. The behavior of the methods is illustrated on a discretization of a nonlinear elliptic partial differential boundary value problem, the minimal surface equation. A conjugate gradient algorithm with splittings is also developed for constrained minimization with upper and lower bounds on the variables, and the method is applied to the obstacle problem for the minimal surface equation.