Min-max disagreements are an important generalization of the correlation clustering problem (CorCP). It can be defined as follows. Given a marked complete graph $G=(V, E)$ , each edge in is by positive label “+” or negative “−” based on similarity connected vertices. The goal to find xmlns:xlink...

We consider a generalized class of relay controllers where the system input may take values in a finite set of constant vectors. A simple continuous-time design method is proposed for linear time invariant (LTI) systems. Furthermore, it is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid containing the origin. The sampling interval...

A generalized Itô formula for time dependent functions of two-dimensional continuous semi-martingales is proved. The formula uses the local time of each coordinate process of the semi-martingale, left space and time first derivatives and second derivative ∇1 ∇ − 2 f only which are assumed to be of locally bounded variation in certain variables, and stochastic Lebesgue-Stieltjes integrals of two...

In an abstract framework, we study local convergence properties of Newton’s method for a sequence of generalized equations which models a discretized variational inequality. We identify conditions under which the method is locally quadratically convergent, uniformly in the discretization. Moreover, we show that the distance between the Newton sequence for the continuous problem and the Newton s...