Robust counterpart optimization techniques are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geome...

Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with n elements (which can be done in 2 n ways), and the notion of choosing a k-element subset of a set with n elements (which can be done in n k ways). In this article I sketch the beginnings of a theory that would import these notions into the category of hedral sets in the sense of Morelli and the cat...

We describe the combination of several novel algorithms into a system which obtains visual motion from a sequence of images and uses it to recover the 3D geometry and 3D motion of polyhedral objects relative to the sensor. The system goes on to use the recovered geometry to recognize the object from a database, a stage which also resolves the depth/speed scaling ambiguity, resulting in absolute...

the radars that use medium prf, have either range ambiguity or doppler ambiguity, but these ambiguities can be resolved with selecting a prf set. avoiding ghost targets detection and minimizing blind zones are two important points that we should consider in targets detection. then, using this set, coincident algorithm and clustering the closely detected points, we resolve ambiguity and detect t...

We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...

We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objec...