Maximal monotone relations and the second derivatives of nonsmooth functions
نویسندگان
چکیده
منابع مشابه
Second Order Cones for Maximal Monotone Operators via Representative Functions
It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T , in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the GraphT . In particular we obtain formula for the Proto-derivative, as well as its polar, the normal cone to the grap...
متن کاملMaximal Monotone Inclusions and Fitzpatrick Functions
We study maximal monotone inclusions from the perspective of (convex) gap functions. We propose a very natural gap function and will demonstrate how this function arises from the Fitzpatrick function — a convex function used effectively to represent maximal monotone operators. • This approach allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. – We...
متن کاملScale-transformations and homogenization of maximal monotone relations with applications
In homogenization, two-scale models arise, e.g., by applying Nguetseng’s notion of two-scale convergence to nonlinear PDEs. A homogenized single-scale problem may then be derived via scale-transformations. A variational formulation due to Fitzpatrick is here used for the scale-integration of two-scale maximal monotone relations, and for the converse operation of scale-disintegration. These resu...
متن کاملMonotone Linear Relations: Maximality and Fitzpatrick Functions
We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick fa...
متن کاملGeneralized Monotone Nonsmooth Maps
Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 1985
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(16)30401-2