Copositive Programming and Related Problems

Foundation of mathematical optimization relies on the urge to utilize available resources to their optimum. This leads to mathematical programs where an objective function is optimized over a set of constraints. The set of constraints can represent different structures, for example, a polyhedron, a box or a cone. Mathematical programs with cone constraints are called cone programs. A sub area of mathematical optimization is the one where the number of variables isfinite while the number of constraints is infinite, known as semi-infinite programming. In the first section of Chapter 1 we will start with a general introduction into the thesis. In the second section some basic definitions are given which are used throughout the thesis. The third and the fourth section provide a brief review of results on cone programming and semi-infinite programming, respectively. In section five we will briefly discuss cone programming relaxations. In the last section we shall give an overview over results presented in the thesis.