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Sufficient conditions for infinite-horizon calculus of variations problems

Joël Blot, Naïla Hayek (2010)

ESAIM: Control, Optimisation and Calculus of Variations

After a brief survey of the literature about sufficient conditions, we give different sufficient conditions of optimality for infinite-horizon calculus of variations problems in the general (non concave) case. Some sufficient conditions are obtained by extending to the infinite-horizon setting the techniques of extremal fields. Others are obtained in a special qcase of reduction to finite horizon. The last result uses auxiliary functions. We treat five notions of optimality. Our problems are essentially motivated...

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

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 problems...

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

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 problems...

Sufficient optimality conditions for multivariable control problems

Andrzej Nowakowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.

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