Nonlinear Preconditioning Techniques for Full-Space Lagrange--Newton Solution of PDE-Constrained Optimization Problems

DOI10.1137/15M104075XzbMath1348.65103MaRDI QIDQ2818260

Haijian Yang, Xiao-Chuan Cai, Feng-Nan Hwang

Publication date: 7 September 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

convergenceboundary controlnumerical resultssequential quadratic programmingincompressible flowsinexact Newton methodflow controlLagrange-Newton algorithmnonlinear elimination preconditionerPDE-constrained optimizations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Quadratic programming (90C20) Newton-type methods (49M15) Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving partial differential equations (49J20) Flow control and optimization for incompressible inviscid fluids (76B75)

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Uses Software

• PETSc

Cites Work

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• Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems
• Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation
• The approximation of boundary control problems for fluid flows with an application to control by heating and cooling
• On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations
• Optimal control of two-and three-dimensional incompressible Navier-Stokes flows
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation
• A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations
• Composing Scalable Nonlinear Algebraic Solvers
• A Nonlinearly Preconditioned Inexact Newton Algorithm for Steady State Lattice Boltzmann Equations
• Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method
• Estimation of Sparse Jacobian Matrices and Graph Coloring Blems
• Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity
• Numerical solution of saddle point problems
• Parallel Multilevel Restricted Schwarz Preconditioners with Pollution Removing for PDE‐Constrained Optimization
• Optimal Control of Thermally Convected Fluid Flows
• Numerical Solution of the Stationary Navier--Stokes Equations Using a Multilevel Finite Element Method
• On Marangoni drying: nonlinear kinematic waves in a thin film
• Globally Convergent Inexact Newton Methods
• Optimal Controls of Navier–Stokes Equations
• The Velocity Tracking Problem for Navier--Stokes Flows With Boundary Control
• Construction of Solution Curves for Large Two-Dimensional Problems of Steady-State Flows of Incompressible Fluids
• Recent Developments in Rayleigh-Bénard Convection
• A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
• Nonlinearly Preconditioned Inexact Newton Algorithms
• Perspectives in Flow Control and Optimization
• An Analysis of Approximate Nonlinear Elimination
• Fully implicit Lagrange–Newton–Krylov–Schwarz algorithms for boundary control of unsteady incompressible flows
• Parallel fully implicit two‐grid methods for distributed control of unsteady incompressible flows
• Field-Split Preconditioned Inexact Newton Algorithms
• Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
• Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange--Newton Solver and Its Application to Optimal Control of Steady Viscous Flows
• Parallel Full Space SQP Lagrange--Newton--Krylov--Schwarz Algorithms for PDE-Constrained Optimization Problems

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