Most of the research pertaining to blocking sets of lines consists of examining existence, structure, and obtaining bounds on the sizes of irreducible blocking sets. In this talk, we will examine several simple irreducible line blocking sets before we explore conic blocking sets. We give an existence theorem for trivial CBSs that relies only on basic properties of planes and conics. We follow this with several recent results about the sizes of minimal CBS and, time permitting, the methods used to obtain these results. Most real-world planning problems contain stochastic elements and require optimization.
Stochastic programming provides an appropriate modeling framework for many such problems.
We describe example applications in a manufacturing system and vehicle routing. Solving such models exactly is often impossible. Deterministically valid approximations and sampling-based estimation techniques play important roles in stochastic optimization. We describe some recent advances in both of these areas. Wavelet expansions are based on translations and dilations of some mother functions.