The Non Smooth Dynamical Systems (NSDS) are a very special kind of dynamical systems characterized by their nonsmoothness in the evolution with respect to time and by a set of non smooth generalized equations. The so-called Moreau’s Sweeping Process[9, 10] is a special kind of differential inclusion with a maximal monotone operator[5] which appears to be a very nice formulation for the unilater...

This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finitedimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of con...

where F is a monotone operator. Recently, Lu et al. [] were concerned with a special class of variational inequalities in which the mapping F is the complement of a nonexpansive mapping and the constraint set is the set of fixed points of another nonexpansive mapping. Namely, they considered the following type of monotone variational inequality (VI) problem: Find x∗ ∈ Fix(T), such that 〈(I –V ...

* Correspondence: hbshigh@yeah. net College of Science, Hebei University of Engineering, Handan 056038, China Full list of author information is available at the end of the article Abstract In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are est...

Many models involve the Coulomb’s law in order to describe dynamical properties of friction phenomena. In order to generalize this Coulomb’s law and to deal with its correct mathematical expression, we study a nonlinear equation where we take into account a maximal monotone graph. In the particular case of Coulomb’s law, existence and uniqueness are proved. But in the general case, only existen...

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex representation of the operator which is a fixed point of this conjugation. 2000 Mathematics Subject Classification: 47H05 keywords: maximal monotone operators, conjugat...

1. Overview This paper talks about that monotone circuit is P-Complete. Decision problem that include P-Complete is mapping that classify input with a similar property. Therefore equivalence relation of input value is important for computation. But monotone circuit cannot compute the equivalence relation of the value because monotone circuit can compute only monotone function. Therefore, I make...

Abstract This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in optimization algorithms and modeling physical systems. The inclusion described a set-valued mapping having property that, for given time instant, describes maximal monotone operator. By successive application proximal operator, we construct sequence functions parameterize...

The sum of (nonlinear) maximal monotone operators is reconsidered from the Yosida approximation and graph-convergence point of view. This leads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maximal monotone. In the case of subdiierentials of convex lower semicontinuous proper functions, the variational sum is eq...

The concept of a monotone operator — which covers both linear positive semi-definite operators and subdifferentials of convex functions — is fundamental in various branches of mathematics. Over the last few decades, several stronger notions of monotonicity have been introduced: Gossez’s maximal monotonicity of dense type, Fitzpatrick and Phelps’s local maximal monotonicity, and Simons’s monoton...