In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

No part of this Journal may be reproduced in any form, by print, photoprint, microolm or any other means without written permission from Abstract This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu's scaled Lip...

Several interior point algorithms have been proposed for solving nonlinear monotone complementarity problems. Some of them have polynomial worst-case complexity but have to connne to short steps, whereas some of the others can take long steps but no polynomial complexity is proven. This paper presents an algorithm which is both long-step and polynomial. In addition, the sequence generated by th...

In this paper we prove the existence of solutions to the following third order differential inclusion:  x(3)(t) ∈ F (t, x(t), ẋ(t), ẍ(t)) + G(x(t), ẋ(t), ẍ(t)), a.e. on [0, T ] x(0) = x0, ẋ(0) = u0, ẍ(0) = v0, and ẍ(t) ∈ S,∀t ∈ [0, T ], where F : [0, T ]×H×H×H → H is a continuous set-valued mapping, G : H× H × H → H is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂g(z) where g...

A finite-dimensional variational inequality parameterized by t ∈ [0, 1] is studied under the assumption that each point of the graph of its generally set-valued solution mapping is a point of strongly regularity. It is shown that there are finitely many Lipschitz continuous functions on [0, 1] whose graphs do not intersect each other such that for each value of the parameter the set of values o...

We study local structure of a nonlinear mapping near points where standard regularity and/or smoothness assumptions need not be satisfied. We introduce a new concept of 2-regularity (a certain kind of second-order regularity) for a once differentiable mapping whose derivative is Lipschitz continuous. Under this 2-regularity condition, we obtain the representation theorem and the covering theore...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

We consider the setting of stochastic bandit problems with a continuum of arms indexed by [0, 1]. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the regret is small with respect to a class of environments that depends on these parameters. This is however not the right perspective, as it i...

Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmüller space equipped with either the Teichmüller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse geometry of these spaces. We show that the quasi-Lipschitz image in X of a box in R is locally near a standard model of a flat in X . As a consequence, we sh...

In this paper, we introduce the extragradient method for finding a common element of the set of solutions of generalized mixed equilibrium problem, the set of common fixed point of family of nonexpansive mappings the set of variational inequality for monotone, Lipschitz continuous mapping in a Hilbert space. Then we prove the strong convergence of iterative algorithm to a common element of this...