In this paper, we consider two geometric optimization problems that are dual to each other and characterize conditions under which the optimal values of the two problems are equal. This characterization relies on establishing separation results for nonconvex sets using general concave surfaces defined in terms of convex augmenting functions. We prove separation results for augmenting functions that are bounded from below, unbounded augmenting functions, and asymptotic augmenting functions.
- Augmenting functions
- Recession directions
- Separation of nonconvex sets
ASJC Scopus subject areas
- General Mathematics
- Computer Science Applications
- Management Science and Operations Research