On Polaroid Intersections

Résumé du livre

Polaroid sets and functions have been introduced as a new tool, with applications in non-linear programming, particularly in quasi-concave and integer optimization problems over a linearly constrained set of feasible solutions. The name polar programming applies to a general class of non-linear mathematical programming problems which can be solved by the polaroid approach. In integer programming polaroids yield non-trivial extensions of the intersection cut approach. The paper builds on the properties of polaroid sets (particularly complete convex polaroids) and focuses on the following intersection problem: Given a point x bar belonging to the polaroid set P*, find the intersection point u* of a one-dimensional ray u with the boundary of P*.