In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we introduce a new uncertainty class ...

Extending and improving some recent results of Hantoute, López, and Zălinescu and others, we provide characterization conditions for subdifferential formulas to hold for the supremum function of a family of convex functions on a real locally convex space.

This paper considers robust stability and robust performance analysis for discrete-time linear systems subject to nonlinear uncertainty. The uncertainty set is described by memoryless, time-invariant, sector bounded, and slope restricted nonlinearities. We first give an overview of the absolute stability criterion based on the Lur’e-Postkinov Lyapunov function, along with a frequency domain con...

Robust optimization is based on the assumption that uncertain data has a convex set as well finite termed uncertainty. The discussion starts with determining robust counterpart, which accomplished by assuming indeterminate in form of boxes, intervals, box-intervals, ellipses, or polyhedra. In this study, counterpart characterized box-interval uncertainty set. formulation also associated master ...

The goal of high-level information fusion is to provide effective decision-support regarding situations, e.g., relations between events. One of the main ways that has been proposed in order to achieve this is to reduce uncertainty regarding the situation by utilizing multiple sources of information. There exist two types of uncertainty: aleatory and epistemic. Aleatory uncertainty, also known a...

This paper develops a segmented real-time dispatch model for power-gas integrated systems (PGISs), where power-to-gas (P2G) devices and traditional automatic generation control units are cooperated to manage wind power uncertainty. To improve the economics of in regard current high operation cost P2Gs, uncertainty set is divided into several segments, linear decision rule developed, which assig...

Often the structure of discrete sets can be described in terms of a closure operator. When each closed set has a unique minimal generating set (as in convex geometries in which the extreme points of a convex set generate the closed set), we have an antimatroid closure space. In this paper, we show there exist antimatroid closure spaces of any size, of which convex geometries are only a sub-fami...

The theme of these lectures is local and global properties of plurisubharmonic functions. First differential inequalities defining convex, subharmonic and plurisubharmonic functions are discussed. It is proved that the marginal function of a plurisubharmonic function is plurisubharmonic under certain hypotheses. We study the singularities of plurisubharmonic functions using methods from convexi...