Convexity and Optimization in Finite Dimensions I

TL;DR: A subadditive dual program for integer programs, and a generalization of R. Gomory's linear inequality characterization of the cuts valid for the group problem are provided.

TL;DR: In this paper, the authors proposed an EM algorithm for maximum likelihood estimation under inequality restrictions A0β ≥ 0, where β is the parameter vector in a linear model W = Xβ + e, and e is an error variable distributed normally with mean zero and a known or unknown variance matrix Σ > 0.

TL;DR: The simplified results, which rely heavily on a careful dissection and improved understanding of the tangent cone of the feasible region of the program, bypass the combinatorial characterization that is intrinsic to B-stationarity.

TL;DR: It is shown that for k = Θ(n), Ω(n log n) is a lower bound to the running time of any algorithm for this problem, and exhibit two algorithms of distinctly different flavors.