Iterative Solution of Augmented Systems Arising in Interior Methods

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual … Read more

Topology optimization of a mechanical component subject to dynamical constraints

This paper is concerned with the optimization of continuum structures under dynamic loading using methods from topology design. The constraint functions are non-linear and implicit, their evaluation requires the resolution of a computation-intensive finite-element analysis performed by a black-box commercial structural mechanics software such as MSC/Nastran. We first present a brief overview of topology optimization … Read more

DIRECT algorithm : A new definition of potentially optimal hyperrectangles

We propose a new version of potentially optimal intervals for the DIRECT algorithm. A two-points based sampling method is presented. The method starts from a distingished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval … Read more

A New Low Rank Quasi-Newton Update Scheme for Nonlinear Programming

A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden … Read more

A copositive programming approach to graph partitioning

We consider 3-partitioning the vertices of a graph into sets $S_1, S_2$ and $S_3$ of specified cardinalities, such that the total weight of all edges joining $S_1$ and $S_2$ is minimized. This problem is closely related to several NP-hard problems like determining the bandwidth or finding a vertex separator in a graph. We show that … Read more