Advances in Optimization and Numerical Analysis

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.

Inhalt

1. Analysis of Interior-Point Methods for Linear Programming Problems with Variable Upper Bounds.- 2. On the Complexity of the Simplex Method.- 3. The Linear Complementarity Problem.- 4. A Direct Search Optimization Method that Models the Objective and Constraint Functions by Linear Interpolation.- 5. A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems.- 6. Performance of a Multifrontal Scheme for Partially Separable Optimization.- 7. Towards Second-Order Methods for Structured Nonsmooth Optimization.- 8. Homotopy Methods in Control System Design and Analysis.- 9. How to Properly Relax Delayed Controls.- 10. On Operator Extensions: the Algebraic Theory Approach.- 11. Global Space-time Finite Element Methods for Time-dependent Convection Diffusion Problems.- 12. Eulerian-Lagrangian Localized Adjoint Methods for Variable-Coefficient Advective-Diffusive-Reactive Equations in Groundwater Contaminant Transport.- 13. The Communication Patterns of Nested Preconditionings for Massively Parallel Architectures.- 14. Smoothness and Superconvergence for Approximate Solutions to the One Dimensional Monoenergetic Transport Equation.- 15. Experiments with the Power and Arnoldi Methods for Solving the Two-Group Neutron Diffusion Eigen-value Problem.- 16. Computational Study of a Free-Boundary Model.- 17. Numerical Approximation to a Class of Weakly Singular Integral Operators.- 18. Directional Second Derivative of the Regularized Function that Smoothes the Min-Max Problem.