Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure … Read more

Discrete convexity and unimodularity. I.

In this article we introduce a theory of convexity for the lattices of integer points, which we call a theory of discrete convexity. In particular, we obtain generalizations of Edmonds’ polymatroid intersection theorem and the Hoffman-Kruskal theorem as consequences of our constructions. Citation Advances in Mathematics (to appear) Article Download View Discrete convexity and unimodularity. … Read more