Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function

Includes bibliographical references (p. 28-29).by Robert M. Freund

On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids

Cataloged from PDF version of article.Given A := {a(1),..., a(m)} subset of R(d) whose affine hull is R(d), we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum-volume enclosing ellipsoid of V. In the case of centrally symmetric sets, we first establish that Khachiyan's barycentric coordinate descent (BCD) method is exactly the polar of the deepest cut ellipsoid method using two-sided symmetric cuts. This observation gives further insight into the efficient implementation of the BCD method. We then propose a variant algorithm which computes an approximate rounding of the convex hull of,91, and which can also be used to compute an approximation to the minimum-volume enclosing ellipsoid of A.. Our algorithm is a modification of the algorithm of Kumar and Yildirim, which combines Khachiyan's BCD method with a simple initialization scheme to achieve a slightly improved polynomial complexity result, and which returns a small "core set." We establish that our algorithm computes an approximate solution to the dual optimization formulation of the minimum-volume enclosing ellipsoid problem that satisfies a more complete set of approximate optimality conditions than either of the two previous algorithms. Furthermore, this added benefit is achieved without any increase in the improved asymptotic complexity bound of the algorithm of Kumar and Yildirim or any increase in the bound on the size of the computed core set. In addition, the "dropping idea" used in our algorithm has the potential of computing smaller core sets in practice. We also discuss several possible variants of this dropping technique. (C) 2007 Elsevier B.V. All rights reserved

Barrier functions and interior-point algorithms for linear programming with zero-, one-, or two-sided bounds on the variables

Includes bibliographical references (p. 37-39).Supported by NSF, AFOSR, and ONR through NSF grant. DMS-8920550 Supported by the Center for Applied Mathematics.Robert M. Freund and Michael J. Todd

Implications of Computational Cognitive Models for Information Retrieval

This dissertation explores the implications of computational cognitive modeling for information retrieval. The parallel between information retrieval and human memory is that the goal of an information retrieval system is to find the set of documents most relevant to the query whereas the goal for the human memory system is to access the relevance of items stored in memory given a memory probe (Steyvers & Griffiths, 2010). The two major topics of this dissertation are desirability and information scent. Desirability is the context independent probability of an item receiving attention (Recker & Pitkow, 1996). Desirability has been widely utilized in numerous experiments to model the probability that a given memory item would be retrieved (Anderson, 2007). Information scent is a context dependent measure defined as the utility of an information item (Pirolli & Card, 1996b). Information scent has been widely utilized to predict the memory item that would be retrieved given a probe (Anderson, 2007) and to predict the browsing behavior of humans (Pirolli & Card, 1996b). In this dissertation, I proposed the theory that desirability observed in human memory is caused by preferential attachment in networks. Additionally, I showed that documents accessed in large repositories mirror the observed statistical properties in human memory and that these properties can be used to improve document ranking. Finally, I showed that the combination of information scent and desirability improves document ranking over existing well-established approaches