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Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.

Regularity and optimal control of quasicoupled and coupled heating processes

Jiří Jarušek (1996)

Applications of Mathematics

Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...

Relaxation of optimal control problems in Lp-SPACES

Nadir Arada (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an Lp-space (p < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Relaxation of optimal control problems in 𝖫 𝗉 -spaces

Nadir Arada (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an L p -space ( p &lt; ∞ ). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Results on existence of solution for an optimal design problem.

Carmen Calvo Jurado, Juan Casado Díaz (2003)

Extracta Mathematicae

In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.

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