The Abadie CQ (ACQ) for convex inequality systems is a fundamental notion in optimization and approximation theory. In terms of the contingent cone and tangent derivative, we extend the Abadie CQ to more general convex multifunction cases and introduce the strong ACQ for both multifunctions and inequality systems. Some seemly unrelated notions are unified by the new ACQ and strong ACQ. Relation...

In this paper, we consider the metric subregularity property for a piecewise linear multifunction (with respect to a piecewise linear constraint) as well as the weak sharp minimum property for a piecewise linear constrained multiobjective optimization problem. Of these properties we pay special attention to the global ones. We first provide a result on a certain relationship between two nonnega...

Multifunction phased array radars have the ability to steer the radar beam electronically, adapting its parameters according to how the radar perceives the environment. Thus, the effective allocation of the available resources is very important. A model of a multifunction phased array radar was implemented to examine the complexities involving this type of radar. Additionally, approaches to ada...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

A temperature controlled 1 Ω–10 kΩ Standard resistors setup was developed at National Institute of Metrological Research, (INRIM). The aim of this realization was the involvement of the setup resistors in the traceability transfer process to high accuracy multifunction electrical instruments used in Secondary Electrical Calibration Laboratories or even their use as primary Standards in high lev...

A well-known equivalence of randomization result of Wald and Wolfowitz states that any Young measure can be regarded as a probability measure on the set of all measurable functions. Here we give a suucient condition for the Young measure to be equivalent to a probability measure on the set of all integrable selectors of a given multifunction. In this way, Aumann's identity for integrals of mult...

This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV , Σ1 and Θ b 2-formulas. We show that the relational surjective pigeonhole principle for Θ2 formulas in S 1 2 implies a circuit block-recognition principle which in turn implies the surjective weak pigeonhole principle for Σ1 formulas. We introduce a class of predicates correspondi...

A new algorithm is proposed for phased array radar search function resource allocation. The proposed algorithm adaptively priorities radar search regions and in overload situations, based on available resources, radar characteristics, maximum range and search regions, optimally allocates radar resources in order to maximize probability of detection. The performance of new algorithm is evaluated...

In Ref.1, extremum problems having in nite-dimensional image have been considered and some preliminary properties have been established. Here we carry on the investigation of such problems and study an optimality condition for the case of unilateral constraints, which partially extends the results of [2,3] to the present type of problems. This is done by associating to the feasible set a specia...