Conjugate gradient algorithms in the solution of optimization problems for nonlinear elliptic partial differential equations

DOI10.1007/BF02246559zbMath0407.65045OpenAlexW2121160976MaRDI QIDQ1258169

Dianne P. O'Leary

Publication date: 1979

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02246559

zbMATH Keywords

EffectivenessConjugate Gradient AlgorithmSplittingsNonlinear Partial Differential EquationsAccelerate ConvergenceComputational AspectsDiscretizationsLarge Systems of Nonlinear EquationsLine Search ProcedureNonlinear Ssor AlgorithmNonquadratic Optimization ProblemNumerical Tests

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Methods of reduced gradient type (90C52) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items

On the efficient solution of nonlinear finite element equations. II. Bound-constrained problems, On multi-grid methods for variational inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A conjugate direction algorithm without line searches
• Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
• Alternative proofs of the convergence properties of the conjugate- gradient method
• Conjugate Gradient Algorithms: Quadratic Termination without Linear Searches
• Partial conjugate gradient methods for a class of optimal control problems
• Convergence conditions for restarted conjugate gradient methods with inaccurate line searches
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Restart procedures for the conjugate gradient method
• Rate of Convergence of Several Conjugate Gradient Algorithms
• Function minimization by conjugate gradients
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Relaxation Methods for Convex Problems
• Numerical Solution of the Minimal Surface Equation
• Efficient Implementations of the Polak–Ribière Conjugate Gradient Algorithm
• Methods of conjugate gradients for solving linear systems