We study when the existence of an increasing selection can be derived from the monotonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending ...

We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunctio...

Abstract – A voltage-mode (VM), multi-input single-output (MISO) type multifunction biquad is proposed. It uses only one operational transresistance amplifier (OTRA) as the active element, while previously reported VM multifunction filters require more OTRAs. Proposed MISO type biquad configuration can realize all five different filter transfer functions. Theoretical results are verified with P...

It is shown that a composite Julia set generated by an infinite array of polynomial mappings is strongly analytic when regarded as a multifunction of the generating maps. An example of such a multifunction, the values of which have Hölder Continuity Property, is constructed. 1

This paper concerns a generalized equation defined by a closed multifunction between Banach spaces, and we employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity (i.e., local error bounds for the concerned multifunction) in general Banach spaces. Following the approach of Ioffe [Trans. Amer. Math. Soc....

The problem of hardware-software partitioning for systems that are being designed as multifunction systems is addressed. Simulated annealing is known to generate very good solutions for most optimization problems, however the running time of this algorithm can be very high. We apply a modified simulated annealing approach to the partitioning problem resulting in a smaller search space, yet yiel...

We quantify the sensitivity of KKT pairs associated with a parameterized family of nonlinear programming problems. Our approach involves proto-derivatives, which are generalized derivatives appropriate even in cases when the KKT pairs are not unique; we investigate what the theory of such derivatives yields in the special case when the KKT pairs are unique (locally). We demonstrate that the gra...

This paper is devoted to the analysis of a special kind of regularity of multifunction which we call metric pseudo-(sub)regularity, when the multifunction is not metrically (sub)regular at a given point but is metrically (sub)regular at certain points in a neighborhood with moduli possibly tending to infinity with a certain order. By using advanced techniques of generalized differentiation we d...

In this paper, we introduce and consider the concept of the prox-regularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or necessary conditions for such a generalized equation to have the metric subregularity in Hilbert s...

M by the proliferation of multifunction products, we investigate product portfolio decisions of a single firm by analyzing the impact of three major factors. First, because multifunction products provide complete or partial functionalities of single-function products, we incorporate substitution or cannibalization effects between the potential products. Second, we explicitly model the variable ...