Accession Number : ADA190029

Title :   Numerical Methods for Linear and Nonlinear Optimization.

Descriptive Note : Final rept. 1 Jul 86-30 Jun 87,

Corporate Author : CALIFORNIA UNIV DAVIS GRADUATE SCHOOL OF ADMINISTRATION

Personal Author(s) : Shanno, David F

PDF Url : ADA190029

Report Date : 16 Sep 1987

Pagination or Media Count : 9

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.

Descriptors :   *NUMERICAL METHODS AND PROCEDURES, *OPTIMIZATION, ALGORITHMS, CODING, COMPUTATIONS, COMPUTER PROGRAMMING, NONLINEAR SYSTEMS, NUMERICAL ANALYSIS, RATES, TEST AND EVALUATION, VARIABLES, QUADRATIC PROGRAMMING, APPROXIMATION(MATHEMATICS)

Subject Categories : Operations Research
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE