The drop theorem,the petal theorem and Ekeland's variational principle

On montre que le principe variationnel d'Ekeland, ou plus precisement, une forme legerement modifiee, est une consequence d'un resultat geometrique connu sous le terme de theoreme de la goutte

[1]  F. Browder.  Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds , 1971 .

[2]  Gérard Lebourg.  Perturbed optimization problems in Banach spaces , 1979 .

[3]  CONTRACTOR DIRECTIONS, DIRECTIONAL CONTRACTORS AND DIRECTIONAL CONTRACTIONS FOR SOLVING EQUATIONS , 1976 .

[4]  F. Browder,et al.  A general principle on ordered sets in nonlinear functional analysis , 1976 .

[5]  G. Isac,et al.  Surjectivity of multifunctions under generalized differentiability assumptions , 1983, Bulletin of the Australian Mathematical Society.

[6]  Tangent cones, starshape and convexity , 1978 .

[7]  Jay S. Treiman.  Characterization of Clarke's tangent and normal cones in finite and infinite dimensions , 1983 .

[8]  A. Brøndsted,et al.  On a lemma of Bishop and Phelps , 1974 .

[9]  J. Caristi,et al.  Fixed point theorems for mapping satisfying inwardness conditions , 1976 .

[10]  Alfred Auslender,et al.  Stability in Mathematical Programming with Nondifferentiable Data , 1984 .

[11]  Ivar Ekeland.  The Hopf-Rinow theorem in infinite dimension , 1978 .

[12]  Halina Frankowska.  The First Order Necessary Conditions for Nonsmooth Variational and Control Problems , 1984 .

[13]  F. Sullivan.  A characterization of complete metric spaces , 1981 .

[14]  A. M. Walker,et al.  Mapping theorems for gateaux differentiable and accretive operators , 1982 .

[15]  J. Aubin,et al.  Fixed points and stationary points of dissipative multivalued maps , 1980 .

[16]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[17]  Jean-Baptiste Hiriart-Urruty,et al.  A Short Proof of the Variational Principle for Approximate Solutions of a Minimization Problem , 1983 .

[18]  R. Temam,et al.  Analyse convexe et problèmes variationnels , 1974 .

[19]  Jean Paul Penot.  A characterization of Clarke’s strict tangent cone via nonlinear semigroups , 1985 .

[20]  M. A. Krasnosel'skii,et al.  Solvability of nonlinear operator equations , 1971 .

[21]  I. Ekeland,et al.  Generic Fréchet-differentiability and perturbed optimization problems in Banach spaces , 1976 .

[22]  R. R. Phelps,et al.  Support cones in Banach spaces and their applications , 1974 .

[23]  A. Ioffe.  Nonsmooth analysis: differential calculus of nondifferentiable mappings , 1981 .

[24]  R. Richardson.  The International Congress of Mathematicians , 1932, Science.

[25]  I. Ekeland.  Nonconvex minimization problems , 1979 .

[26]  J. Borwein.  Stability and regular points of inequality systems , 1986 .

[27]  R. Rockafellar.  Directionally Lipschitzian Functions and Subdifferential Calculus , 1979 .

[28]  I. Ekeland.  On the variational principle , 1974 .

[29]  A. Ioffe.  Regular points of Lipschitz functions , 1979 .