We consider multifunctions acting between two linear normed spaces and having closed convex images. Approximations are considered which serve as an expansion of it. Generalized delta theorems for random sets in in nite dimensions are shown using those approximations. Furthermore, univalued, resp. Castaing representations of the multifunction are constructed with (higher order) di erentiability ...

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

Recently, Bertsekas and Tsitsiklis proposed a partially asynchronous implementation of the gradient projection algorithm of Goldstein and Levitin and Polyak for the problem of minimizing a differentiable function over a closed convex set. In this paper, we analyze the rate of convergence of this algorithm. We show that if the standard assumptions hold (that is, the solution set is nonempty and ...

In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous ...

This paper studies stability of user-equilibrium (UE) route flow solutions with respect to inputs to a traffic assignment problem, namely the travel demand and parameters in the link cost function. It shows, under certain continuity and strict monotonicity assumptions on the link cost function, that the UE link flow is a continuous function of the inputs, that the set of UE route flows is a con...

The use of microprocessor based multifunction relays is on the increase due to the advantages they offer such as communications, measurements, simplified wiring, and reduced space requirements. Since many protection functions are included in one device however, there has been some concern about providing adequate protection should a multifunction relay fail. A reliable protection scheme is very...

Title of dissertation: DISTRIBUTED OPTIMIZATION OF RESOURCE ALLOCATION FOR SEARCH AND TRACK ASSIGNMENT WITH MULTIFUNCTION RADARS Tracie A. Severson, Doctor of Philosophy, 2013 Dissertation directed by: Dr. Derek A. Paley Department of Aerospace Engineering and the Institute for Systems Research The long-term goal of this research is to contribute to the design of a conceptual architecture and f...

Let σ be a positive number and Cσ := C([−σ, 0], R) the Banach space of continuous functions from [−σ, 0] into R and let T (t) be the operator from C([−σ, T ], R) into Cσ, defined by (T (t)x)(s) := x(t + s), s ∈ [−σ, 0]. We prove the existence of solutions for functional differential inclusion(differential inclusions with memory) x′ ∈ F (T (t)x) + f(t, T (t)x) where F is upper semicontinuous, co...

We consider whether the “inequality-splitting” property established in the Brøndsted– Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an “inequality-splitting” property does hold. These multifunctions...