Primal-Dual Strategy for Constrained Optimal Control Problems

From MaRDI portal
Publication:4253029

DOI10.1137/S0363012997328609zbMath0937.49017OpenAlexW1977135073MaRDI QIDQ4253029

Kazufumi Ito, Bergounioux, Maïtine, Karl Kunisch

Publication date: 24 June 1999

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0363012997328609




Related Items

Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problemsVariational and virtual discretizations of optimal control problems governed by diffusion problemsOn convergence of a receding horizon method for parabolic boundary controlParametric sensitivity analysis in optimal control of a reaction-diffusion system – part II: practical methods and examplesPreconditioning nonlocal multi-phase flowA \(P_1\) finite element method for a distributed elliptic optimal control problem with a general state equation and pointwise state constraintsOn Instantaneous Control for a Nonlinear Parabolic Boundary Control ProblemPrimal-dual active-set method for solving the unilateral pricing problem of American better-of options on two assetsA new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problemsA cubic \(C^{\mathbf{0}}\) interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraintsSuperconvergence Properties for Optimal Control Problems Discretized by Piecewise Linear and Discontinuous FunctionsOptimal control of the convection-diffusion equation using stabilized finite element methodsPreconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control ProblemsThe semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalizationA family of second-order methods for convex \(\ell _1\)-regularized optimizationAn interior point method designed for solving linear quadratic optimal control problems withhpfinite elementsError estimates for the discretization of elliptic control problems with pointwise control and state constraintsElliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devicesRegularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditionsPreconditioning PDE-constrained optimization with \(L^1\)-sparsity and control constraintsActive-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous MediaA priori error estimates for elliptic optimal control problems with a bilinear state equationUnnamed ItemEnergy corrected FEM for optimal Dirichlet boundary control problemsReliable a posteriori error estimation for state-constrained optimal controlA preconditioned MinRes solver for time-periodic parabolic optimal control problemsA partition of unity method for a class of fourth order elliptic variational inequalitiesAnalysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problemsA lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problemA Semismooth Newton Multigrid Method for Constrained Elliptic Optimal Control ProblemsA Feasible Active Set Method for Strictly Convex Quadratic Problems with Simple BoundsA new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preservingModel Reduction by Adaptive Discretization in Optimal ControlNumerical analysis for the pure Neumann control problem using the gradient discretisation methodRegularization of inverse problems via box constrained minimizationA priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equationsAn A Posteriori Analysis of $C^0$ Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff PlatesHigh accuracy analysis of nonconforming MFEM for constrained optimal control problems governed by Stokes equationsGoal-oriented a posteriori error estimation for Dirichlet boundary control problemsDiscretization of Optimal Control ProblemsA Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control ProblemsMultigrid methods for parabolic distributed optimal control problemsA fuzzy system based active set algorithm for the numerical solution of the optimal control problem governed by partial differential equationStochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficientsOptimal control problem of the two-dimensional modified anomalous subdiffusion equation with discontinuous Galerkin approximationPrimal-dual active set method for pricing American better-of option on two assetsAdaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inferenceThird order convergent time discretization for parabolic optimal control problems with control constraintsMimetic discretizations of elliptic control problemsPreconditioning for Allen-Cahn variational inequalities with non-local constraintsAdaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equationsAdditive Schwarz preconditioners for the obstacle problem of clamped Kirchhoff platesInverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical RealizationRobust error estimates for the finite element approximation of elliptic optimal control problemsPrimal-dual active set strategy for large scale optimization of cardiac defibrillationError bounds for discontinuous finite volume discretisations of Brinkman optimal control problemsAdaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equationsAn efficient duality-based approach for PDE-constrained sparse optimizationOn the interplay between interior point approximation and parametric sensitivities in optimal controlAdaptive finite element method for elliptic optimal control problems: convergence and optimalityPrimal-dual interior-point methods for PDE-constrained optimizationFinite element approximation of optimal control problem governed by space fractional equationRegularization for semilinear elliptic optimal control problems with pointwise state and control constraintsA multigrid method for constrained optimal control problemsFinite element method for a nonsmooth elliptic equationNonconvergence of the plain Newton-min algorithm for linear complementarity problems with a \(P\)-matrixConstrained optimal control of Navier--Stokes flow by semismooth Newton methodsSolving discretized degenerate optimal control problems with state constraintsVariational discretization of Lavrentiev-regularized state constrained elliptic optimal control problemsDiscrete concepts versus error analysis in PDE-constrained optimizationAlgorithms for PDE-constrained optimizationOptimal control of PDEs with regularized pointwise state constraintsNumerical analysis for the approximation of optimal control problems with pointwise observationsPreconditioned Solution of State Gradient Constrained Elliptic Optimal Control ProblemsA partition of unity method for the displacement obstacle problem of clamped Kirchhoff platesA regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraintsThe Nonnegative Matrix Factorization: Regularization and ComplexityLagrange optimality system for a class of nonsmooth convex optimizationError estimates for linear-quadratic control problems with control constraintsA finite element method for an elliptic optimal control problem with integral state constraintsParameter-robust preconditioning for the optimal control of the wave equationSharp Interface Limit for a Phase Field Model in Structural OptimizationStrategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environmentSource representation strategy for optimal boundary control problems with state constraintsProjection onto a Polyhedron that Exploits SparsityRegularized state-constrained boundary optimal control of the Navier-Stokes equationsAn ADMM numerical approach to linear parabolic state constrained optimal control problemsA new marking strategy for the adaptive finite element approximation of optimal control constrained problemsNon-commutative discretize-then-optimize algorithms for elliptic PDE-constrained optimal control problemsGlobally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem SolvesEfficient block preconditioners for integral constrained elliptic optimal control problems with finite element approximations\(P_1\) finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditionsSolving elliptic control problems with interior point and SQP methods: Control and state constraintsA semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equationsA globally convergent primal-dual active-set framework for large-scale convex quadratic optimizationPost-processing procedures for an elliptic distributed optimal control problem with pointwise state constraintsAn all-at-once approach for the optimal control of the unsteady Burgers equationSuperconvergence for Neumann boundary control problems governed by semilinear elliptic equationsError estimates for the numerical approximation of boundary semilinear elliptic control prob\-lemsDirichlet control of elliptic state constrained problemsSmoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control ProblemsRapid Solution of Minimal Riesz Energy ProblemsA New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State ConstraintsAn Extension of the Projected Gradient Method to a Banach Space Setting with Application in Structural Topology OptimizationAdaptive Symmetric Interior Penalty Galerkin Method for Boundary Control ProblemsA Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator EquationsBDF2 schemes for optimal parameter control problems governed by bilinear parabolic equationsAdditive Schwarz preconditioners for C0 interior penalty methods for the obstacle problem of clamped Kirchhoff platesA perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility MappingA symmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraintsPrimal-Dual Active-Set Method for the Valuation Of American Exchange OptionsA modified combined active-set Newton method for solving phase-field fracture into the monolithic limitPrimal-Dual Active Set Method for American Lookback Put Option PricingThe Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach SpacesA Joint Tikhonov Regularization and Augmented Lagrange Approach for Ill-Posed State Constrained Control Problems with Sparse ControlsOptimal control of coupled multiphysics problems: Guidelines for real-life applications demonstrated for a complex fuel cell modelOptimization methods for Dirichlet control problemsA morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraintsPreconditioning for partial differential equation constrained optimization with control constraintsAdaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraintsUnnamed ItemA Partition of Unity Method for the Obstacle Problem of Simply Supported Kirchhoff PlatesA Primal-Dual Active Set Method for Bilaterally Control Constrained Optimal Control of the Navier–Stokes EquationsFINITE DIFFERENCE SMOOTHING SOLUTIONS OF NONSMOOTH CONSTRAINED OPTIMAL CONTROL PROBLEMSGoal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control ProblemsSemi–Smooth Newton Methods for Variational Inequalities of the First KindA leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problemsLinear and Discontinuous Approximations for Optimal Control ProblemsOn regularization methods for the numerical solution of parabolic control problems with pointwise state constraintsPrimal–dual active set method for control constrained optimal control of the Stokes equationsPreconditioners for state-constrained optimal control problems with Moreau-Yosida penalty functionAn Algorithmic Characterization of P-matricity II: Adjustments, Refinements, and ValidationAn Inexact Uzawa Algorithmic Framework for Nonlinear Saddle Point Problems with Applications to Elliptic Optimal Control ProblemOn the uniqueness of non-reducible multi-player control problemsApplication of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and BeyondA C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraintsDiscontinuous Finite Volume Element Methods for the Optimal Control of Brinkman Equations