Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
Computational Optimization and Applications
Discrete Applied Mathematics
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
Many applications in the area of production and statistical estimation are problems of convex optimization subject to ranking constraints that represent a given partial order. This problem, which we call the convex cost closure (CCC) problem, is a generalization of the known maximum (or minimum) closure problem and the isotonic regression problem. For a CCC problem on n variables and m constraints we describe an algorithm that has the complexity of the minimum cut problem plus the complexity of finding the minima of up to n convex functions. Since the CCC problem is a generalization of both minimum cut and minimization of n convex functions, this complexity is the fastest one possible. For the quadratic problem the complexity of our algorithm is strongly polynomial, $O(mn\log {\frac{n^2}{m}})$. For the isotonic regression problem the complexity is O(n log U,) for U the largest range for a variable value.