Nonsmooth Optimization and Related TopicsF.H. Clarke, Vladimir Fedorovich Demʹi︠a︡nov, F. Giannessi This volume contains the edited texts of the lect. nres presented at the International School of Mathematics devoted to Nonsmonth Optimization, held from . June 20 to July I, 1988. The site for the meeting was the "Ettore Iajorana" Centre for Sci- entific Culture in Erice, Sicily. In the tradition of these meetings the main purpose was to give the state-of-the-art of an important and growing field of mathematics, and to stimulate interactions between finite-dimensional and infinite-dimensional op- timization. The School was attended by approximately 80 people from 23 countries; in particular it was possible to have some distinguished lecturers from the SO\-iet Union, whose research institutions are here gratt-fnlly acknowledged. Besides the lectures, several seminars were delivered; a special s- ssion was devoted to numerical computing aspects. The result was a broad exposure. gi -. ring a deep knowledge of the present research tendencies in the field. We wish to express our appreciation to all the participants. Special mention 5hould be made of the Ettorc;. . Iajorana Centre in Erice, which helped provide a stimulating and rewarding experience, and of its staff which was fundamental for the success of the meeting. j\, loreover, WP want to extend uur deep appreci |
Contents
Scalar and vector generalized convexity E Castagnoli and P Mazzoleni 1 Introduction | 1 |
Generalized concavity for scalar functions | 2 |
Generalized concavity for vector functions | 3 |
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Nonsmooth Optimization and Related Topics F.H. Clarke,Vladimir F. Dem'yanov,F. Giannessi Limited preview - 2013 |
Nonsmooth Optimization and Related Topics Francis Clarke,Vladimir F. Dem'yanov,Franco Giannessi No preview available - 2014 |
Nonsmooth Optimization and Related Topics F.H. Clarke,Vladimir F. Dem'yanov,F. Giannessi No preview available - 2013 |
Common terms and phrases
algorithm assume assumption Banach space C₁ calculus closed convex codifferentiable concave cone approximations consider constraints continuous convergence Convex analysis convex cone convex function convex set defined definition denote differentiable directional derivative Example exists F.H. Clarke finite formula function f fuzzy global minimum gradient h(xo H₁ hence Hestenes holds implies inequality inf sup K₁ Lemma lim inf lim sup linear Lipschitzian local minimum lower semicontinuous Math Mathematics maximum minimization minimum point necessary condition neighbourhood nonconvex nondifferentiable nonempty nonlinear programming nonsmooth obtain optimal control optimal solutions optimal trajectory optimization problems penalty function problem 1.1 Proof properties Proposition prove proximal normal quadratic R.T. Rockafellar satisfied Section sequence space Stackelberg subdifferential subgradient subset sufficient conditions sup inf tangent cone Theorem topology u₁ upper v₁ value function vector windshear