Kenneth E. Hillstrom

Testing Unconstrained Optimization Software

Much of the testing of optimization software is inadequate because the number of test functmns is small or the starting points are close to the solution. In addition, there has been too much emphasm on measurmg the efficmncy of the software and not enough on testing reliability and robustness. To address this need, we have produced a relatwely large but easy-to-use collection of test functions and designed gmdelines for testing the reliability and robustness of unconstrained optimization software.

A Simulation Test Approach to the Evaluation of Nonlinear Optimization Algorithms

A simulation test methodology was developed to evaluate unconstrained nonlinear optimization computer algorithms. The test technique simulates problems optimization algorithms encounter in practice by employing a repertoire of problems representing various topographies (descending curved valleys, saddle points, ridges, etc.), dimensions, degrees of nonlinearity (e.g., linear to exponential) and minima, addressing them from various randomly generated initial approximations to the solution and recording their performances in the form of statistical summaries. These summaries, consisting of categorized results and statistical averages, are generated for each algorithm as tested over members of the problem set. The individual tests are composed of a series of runs from random starts over a member of the problem set. Descriptions of the test technique, test problem, and test results are provided. 3 figures, 2 tables.

Algorithm 566: FORTRAN Subroutines for Testing Unconstrained Optimization Software [C5], [E4]

A partial listing of the FORTRAN package of subroutines for testing unconstrained optimazation software is given with a brief description of the subroutines. The following three problem areas are considered: (1) zeros of systems of N nonlinear functions in N variables; (2) least square minimization of M nonlinear functions in N variables; (3) unconstrained minimization of an objective function with N variables. To test a code in any of the three problem areas, the user must provide a driver and interface routine. The package includes example drivers and interface routines for each of the problem areas. Sample data are also provided. (SC)

Comparison of several adaptive Newton-Cotes quadrature routines in evaluating definite integrals with peaked integrands

This report compares the performance of five different adaptive quadrature schemes, based on Newton-Cotes (2<italic>N</italic> + 1) point rules (<italic>N</italic> = 1, 2, 3, 4, 5), in approximating the set of definite integrals ∫<supscrpt>1</supscrpt><subscrpt>-1</subscrpt> (<italic>x</italic><supscrpt>2</supscrpt> + <italic>p</italic><supscrpt>2</supscrpt>)<supscrpt>-1</supscrpt> <italic>dx</italic> with relative accuracy ε.

Certification of algorithm 257: Havie integrator

if abs(F[Ll-Fapprox[L]) > epsilon X abs(F[L]) then begin for k := O step 1 until Lmax do Fapprox[k] := F[k];