A quadratically constrained minimization problem arising from PDE of Monge-Ampère type

DOI10.1007/s11075-009-9300-5zbMath1187.65073OpenAlexW2077827311MaRDI QIDQ849146

Roland Glowinski, Danny C. Sorensen

Publication date: 24 February 2010

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9300-5

zbMATH Keywords

algorithmconvergencenumerical exampleDirichlet problemeigenvalue minimizationquadratic constraintselliptic Monge-Ampère equation\(\sigma_2\)-operatorleast-squares minimization

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Estimates of eigenvalues in context of PDEs (35P15) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Discrete approximations in optimal control (49M25) Monge-Ampère equations (35J96)

Related Items

A least-squares/relaxation method for the numerical solution of the three-dimensional elliptic Monge-Ampère equation, Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Ampère equation, A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation, An Alternating Direction Method of Multipliers for the Numerical Solution of a Fully Nonlinear Partial Differential Equation Involving the Jacobian Determinant, On the Numerical Solution of the Dirichlet Problem for the Elliptic $$(\sigma _2)$$ ( σ 2 ) Equation, A Numerical Algorithm for a Fully Nonlinear PDE Involving the Jacobian Determinant

Cites Work

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• General solutions of the Monge-Ampère equation in \(n\)-dimensional space
• On the numerical solution of a two-dimensional Pucci's equation with Dirichlet boundary conditions: a least-squares approach