We give a pattern search method for nonlinearly constrained optimization that is an adaption of a bound constrained augmented Lagrangian method first proposed by Conn, Gould, and Toint [SIAM J. Numer. Anal., 28 (1991), pp. 545–572]. In the pattern search adaptation, we solve the bound constrained subproblem approximately using a pattern search method. The stopping criterion proposed by Conn, Go...

Stephen Jay Gould is rightly remembered for many different kinds of contributions to our intellectual life. I focus on his criticisms of uses of evolutionary ideas to defend inegalitarian doctrines and on his attempts to expand the framework of Darwinian evolutionary theory. I argue that his important successes in the former sphere are applications of the idea of local critique, grounded in car...

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(ǫ) proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an ǫ-approximate first-order critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where high-order derivatives are used...

The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block structure in which the (2,2) block (denoted by −C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the ...