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second-orderoptimality conditions

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Second-order sufficient optimality conditionsfor the optimal control of Navier-Stokes equations
Fredi Tröltzsch, Daniel Wachsmuth
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 1 / January 2006

Published online by Cambridge University Press:

15 December 2005, pp. 93-119

Print publication:

January 2006
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In this paper sufficient optimality conditions are established for optimal control ofboth steady-state and instationary Navier-Stokes equations. The second-order condition requirescoercivity of the Lagrange function on a suitable subspace together with first-order necessaryconditions. It ensures local optimality of a reference function in a Ls -neighborhood, whereby the underlying analysis allows to use weaker norms than L∞ .