Geodesic
Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities
Serdica Mathematical Journal, Tome 21 (1995) no. 3, pp. 185-200 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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The author recently introduced a regularity assumption for derivatives of set-valued mappings, in order to obtain first order necessary conditions of optimality, in some generalized sense, for nondifferentiable control problems governed by variational inequalities. It was noticed that this regularity assumption can be viewed as a symmetry condition playing a role parallel to that of the wellknown symmetry property of the Hessian of a function at a given point. In this paper, we elaborate this point in a more detailed way and discuss some related questions. The main issue of the paper is to show (using this symmetry condition) that necessary conditions of optimality alluded above can be shown to be also sufficient if a weak pseudo-convexity assumption is made for the subgradient operator governing the control equation. Some examples of application to concrete situations are presented involving obstacle problems.
Keywords: Set-Valued Mapping, Proto-Derivative, Subgradient Operator, Pseudo-Convexity, Closed Convex Process, Optimality Condition, Variational Inequality 
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     author = {Ndoutoume, James},
     title = {Sufficient {Conditions} of {Optimality} for {Control} {Pproblem} {Governed} by {Variational} {Inequalities}},
     journal = {Serdica Mathematical Journal},
     pages = {185--200},
     year = {1995},
     volume = {21},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_1995_21_3_a1/}
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Ndoutoume, James. Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities. Serdica Mathematical Journal, Tome 21 (1995) no. 3, pp. 185-200. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_3_a1/