Optimal transport, shape optimization and global minimization

DOI10.1016/j.crma.2007.03.015zbMath1115.65075OpenAlexW1979539698MaRDI QIDQ883521

Bijan Mohammadi

Publication date: 4 June 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2007.03.015

zbMATH Keywords

numerical examplesboundary value problemsshape optimizationglobal solutionsglobal minimizationoptimal transport problems

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items (8)

Numerical upper bounds on growth of automaton groups ⋮ Isogeometric Method for the Elliptic Monge-Ampère Equation ⋮ A finite element/operator-splitting method for the numerical solution of the two dimensional elliptic Monge-Ampère equation ⋮ On standard finite difference discretizations of the elliptic Monge-Ampère equation ⋮ A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation ⋮ Improving the identification of general Pareto fronts by global optimization ⋮ Spline element method for Monge-Ampère equations ⋮ On the Numerical Solution of the Dirichlet Problem for the Elliptic $$(\sigma _2)$$ ( σ 2 ) Equation

Cites Work

• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: a least-squares approach
• Numerical solution of the Monge--Ampère equation by a Newton's algorithm
• A dynamical approach to convex minimization coupling approximation with the steepest descent method
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Semideterministic global optimization method: Application to a control problem of the Burgers equation
• A variational model for urban planning with traffic congestion
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