Displaying similar documents to “Proximal smoothness and the lower- C 2 property.”

Abstract Subdifferential Calculus and Semi-Convex Functions

Ivanov, Milen, Zlateva, Nadia (1997)

Serdica Mathematical Journal

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∗ The work is partially supported by NSFR Grant No MM 409/94. We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function.

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Brohe, M., Tossings, P. (2000)

Serdica Mathematical Journal

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Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of...

Lower semicontinuous differential inclusions

Tzanko Donchev (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

Deville, Robert (1995)

Serdica Mathematical Journal

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We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive...

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

Radu Ioan Boţ, Sorin-Mihai Grad (2011)

Open Mathematics

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In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation...

A-monotone nonlinear relaxed cocoercive variational inclusions

Ram Verma (2007)

Open Mathematics

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Based on the notion of A - monotonicity, a new class of nonlinear variational inclusion problems is presented. Since A - monotonicity generalizes H - monotonicity (and in turn, generalizes maximal monotonicity), results thus obtained, are general in nature.