SIAM Journal on Control and Optimization
Computational Optimization and Applications
Computational Optimization and Applications
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
Feasible and Noninterior Path-Following in Constrained Minimization with Low Multiplier Regularity
SIAM Journal on Control and Optimization
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Computational Optimization and Applications
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Primal-dual interior-point methods for PDE-constrained optimization
Mathematical Programming: Series A and B
Computational Optimization and Applications
Barrier Methods for Optimal Control Problems with State Constraints
SIAM Journal on Optimization
SIAM Journal on Optimization
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In this work we consider the optimal control problem of a semilinear elliptic partial differential equation (PDE) with a Dirichlet boundary condition, where the control variable is distributed over the domain and is constrained to be nonnegative. The approach is to consider an associated family of penalized problems, parametrized by $\varepsilon0$, whose solutions define a central path converging to the solution of the original problem. Our aim is to obtain an asymptotic expansion for the solutions of the penalized problems around the solution of the original problem. This approach allows us to recover some known error bounds for the logarithmic barrier approximation and to obtain some new ones for a rather general class of barrier functions. In this manner, we generalize the results of [F. Alvarez et al., Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems, Math. Program. Ser. A, to appear], which were obtained in the ordinary differential equation (ODE) framework.