Nash, Stephen G. | Search NASA

DOE OSTI2013

Optimization Algorithms for Hierarchical Problems, with Applications to Nanoporous Materials

The aim of the overall project was research to formulate and solve multi-scale optimization problems for energy storage applications. More specifically, we formulated multi-scale models for optimizing the internal structure of nanoporous materials, with the goal of developing models for related energy applications associated with sustainable sources of energy. The applications include supercapacitors, hydrogen storage, catalytic beds, and filters. The optimization algorithms we have developed can be applied to general hierarchical design problems arising from complex systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗