Numerical Methods for Linear and Nonlinear Optimization.

Abstract

Three major objectives were completed during the year. The first demonstrates how to directly use rank-one updates to a Cholesky factorization of the required inverse for Karmarkar projections while fully exploiting sparsity. This can significantly improve computational speed when only a few variables are changing significantly at each step. The second demonstrates a new method for adding new variables to a quasi-Newton Hessian approximation which preserves problem scale and positive definiteness of the Hessian. Numerical results show the method to be preferable to known methods. The third examines a variety of ways of implementing a sequential quadratic programming code, and uses numerical testing to indicate a suitable merit function and good algorithms for updating Lagrange multiplier and Hessian approximations. Recent new results for updating Hessians for unconstrained problems are currently being studied to determine if better Hessian approximations can be obtained.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 16, 1987
Accession Number
ADA190029

Entities

People

  • David F. Shanno

Organizations

  • University of California, Davis

Tags

DTIC Thesaurus Topics

  • Algorithms
  • California
  • Computations
  • Computer Programming
  • Evolutionary Algorithms
  • Lagrangian Functions
  • Linear Programming
  • Mathematical Programming
  • Nonlinear Programming
  • Numerical Analysis
  • Optimization
  • Quadratic Programming
  • Schools
  • Security
  • Universities

Readers

  • Operations Research