Second-order necessary conditions for discrete inclusions with end point constraints
We study an optimization problem given by a discrete inclusion with end point constraints. An approach concerning second-order optimality conditions is proposed.
Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a -neighborhood, whereby the underlying analysis allows to use weaker norms than .
Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a Ls-neighborhood, whereby the underlying analysis allows to use weaker norms than L∞.
Solution to a semilinear problem on type II regions determined by the Fučik spectrum.
Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality
In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...
Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss
Sufficient condition for Pareto optimization in Banach spaces