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This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension,… (More)
This work shows that the BFGS method and other methods in the Broyden class, with exact line searches, may fail for non-convex objective functions.
We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after… (More)
In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each… (More)
We present two examples in which the dual affine scaling algorithm converges to a vertex that is not optimal if at each iteration we move 0.999 of the step to the boundary of the feasible region.
We discuss the convergence of line search methods for minimization. We explain how Newton’s method and the BFGS method can fail even if the restrictions of the objective function to the search lines… (More)
Dedicated to our friends Beresford and Velvel on the occasion of their sixtieth birthdays. ABSTRACT We show that a certain matrix norm ratio studied by Parlett has a supremum that is O(p n) when the… (More)