Displaying similar documents to “Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities”

Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities

Karl Kunisch, Daniel Wachsmuth (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimality conditions are derived for the regularized ...

Minimal invasion: An optimal L∞ state constraint problem

Christian Clason, Kazufumi Ito, Karl Kunisch (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is...

Minimal invasion: An optimal L state constraint problem

Christian Clason, Kazufumi Ito, Karl Kunisch (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization...