Optimal control of semilinear multistate systems with state constraints
SIAM Journal on Control and Optimization
Optimal damping control and nonlinear elliptic systems
SIAM Journal on Control and Optimization
Boundary control of semilinear elliptic equations with pointwise state constraints
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Augmented Lagrangian--SQP Methods for Nonlinear OptimalControl Problems of Tracking Type
SIAM Journal on Control and Optimization
Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Study of an Optimal Control Problem for Diffusive Nonlinear Elliptic Equations of Logistic Type
SIAM Journal on Control and Optimization
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Computational Optimization and Applications
Solving elliptic control problems with interior point and SQP methods: control and state constraints
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
SIAM Journal on Control and Optimization
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Computational Optimization and Applications
Computational Optimization and Applications
Inner solvers for interior point methods for large scale nonlinear programming
Computational Optimization and Applications
Some iterative methods for the solution of a symmetric indefinite KKT system
Computational Optimization and Applications
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
On two numerical methods for state-constrained elliptic control problems
Optimization Methods & Software
Computational Optimization and Applications
Optimal Solvers for PDE-Constrained Optimization
SIAM Journal on Scientific Computing
A note on the approximation of elliptic control problems with bang-bang controls
Computational Optimization and Applications
SIAM Journal on Control and Optimization
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Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distributed control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local Pontryagin minimum principle. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. The problems are formulated as AMPL (R. Fourer, D.M. Gay, and B.W. Kernighan, “AMPL: A modeling Language for Mathematical Programming”, Duxbury Press, Brooks-Cole Publishing Company, 1993) scripts and several optimization codes are applied. In particular, it is shown that a recently developed interior point method is able to solve theses problems even for high discretizations. Several numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for different types of controls including bang–bang controls. The necessary conditions of optimality are checked numerically in the presence of active control and state constraints.