The literature in the field of interior point methods for Linear Programming has been almost exclusively algorithmic oriented. Very few contributions have been made towards the theory of Linear Programming itself. In particular none of them offer a simple, self-contained introduction to the...

The comparison of increasing doses of a compound to a zero dose control is of interest in medical and toxicological studies. Assume that the mean dose effects are non-decreasing among the non-zero doses of the compound. A simple procedure that modifies Dunnett's procedure is proposed to...

Alvo and Cabilio [Alvo, M., Cabilio, P., 1995b. Testing ordered alternatives in the presence of incomplete data. J. Amer. Statist. Assoc. 90, 1015-1024] extended the Page and Jonckheere tests when randomized blocks are incomplete. Here we use the step-down testing procedure of Marcus...

Dykstra and Robertson [1983. On testing monotone tendencies. J. Amer. Statist. Assoc. 78, 342-350] proposed the likelihood ratio tests for testing "decreasing on the average" which is closely related to the "starshaped ordering" discussed in Shaked [1979. Estimation of starshaped sequences of...

Euclidean Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the full-Newton step infeasible interior-point method for linear optimization of Roos [Roos, C., 2006. A full-Newton step O(n)...

In this paper, we consider convex optimization problems with cone constraints (CPC in short). We study generalized weak sharp minima properties for (CPC) in the Banach space and Hilbert space settings, respectively. Some criteria and characterizations for the solution set to be a set of...