Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards Boulder, Colorado January 5–6, 1981

ISBN-13: 9783540114956 / Angielski / Miękka / 1982 / 384 str.

J.M. Mulvey

Opis

2. APL 3+5 Dyadic functions sucb as +, -, x, +, *, r (max), 8 L (min), and e (log) operate on scalars and 3 4 2+5 1 7 extend to arrays in a systematic manner. Two 8 5 9 array arguments of a function must bave tbe same 3+5 1 7 :shape (ie, vectors must bave tbe same number of 8 4 10 elements, matrices must bave tbe same number of 3r5 1 7 rows and columns). If one argument of a function 5 3 7 is a scalar, it is applied to eacb element of tbe 1 2 3*2 otber argument. 4 1 9 2e1 2 4 8 16 0 2 3 4 1 M 1 2 3 4 5 6 Mx2 2 4 6 8 10 12 M+M 2 4 6 8 10 12 -5 -3 0 2 Monadia funations such as -, I, x -3 5 o 2 (signum), r (ceiling, Le., small- x3 -5 0 2 est integer greater or equal to o -1 1 1 number) ,L (floor, i.e., largest -2.1 r3.5 2 integer less than or equal to -2 4 2 nUllwer) and 0 (pi times) operate -2.1 L3.5 2 on arrays and produce results 3 3 2 with the same shape as the argu- 01 2 3 ment. 3.1416 6.2832 9.4248 3=3 R~/QtionQI functions follow the same rules. The 1 result is 1 for true, 0 for false.

Spis treści

Opening Address.- 1. Design and Use of Problem Generators and Hand Selected Test Cases.- Test problems for computational experiments -- issues and techniques.- NETGEN-II: A system for generating structured network-based mathematical programming test problems.- The definition and generation of geometrically random linear constraint sets.- Construction of nonlinear programming test problems with known solution characteristics.- A comparison of real-world linear programs and their randomly generated analogs.- 2. Nonlinear Optimization Codes and Empirical Tests.- Evidence of fundamental difficulties in nonlinear optimization code comparisons.- A statistical review of the Sandgren-Ragsdell comparative study.- A methodological approach to testing of NLP-software.- 3. Integer Programming and Combinatorial Optimization.- A computational comparison of five heuristic algorithms for the Euclidean traveling salesman problem.- Implementing an algorithm: performance considerations and a case study.- Which options provide the quickest solutions.- An integer programming test problem generator.- 4. Comparative Computational Studies in Mathematical Programming.- Remarks on the evaluation of nonlinear programming algorithms.- Comments on evaluating algorithms and codes for mathematical programming.- Some comments on recent computational testing in mathematical programming.- Remarks on the comparative experiments of Miele, Sandgren and Schittkowski.- 5. Testing Methodologies.- In pursuit of a methodology for testing mathematical programming software.- Nonlinear programming methods with linear least squares subproblems.- An outline for comparison testing of mathematical software -- illustrated by comparison testings of software which solves systems of nonlinear equations.- A portable package for testing minimization algorithms.- 6. Approaches to Software Testing from Other Disciplines.- Transportable test procedures for elementary function software.- Testing and evaluation of statistical software.- TOOLPACK -- An integrated system of tools for mathematical software development.- Overview of testing numerical software.- The application of Halstead’s software science difficulty measure to a set of programming projects.- 7. Special Topics.- Mathematical programming algorithms in APL.- 8. Advances in Networks.- Solution strategies and algorithm behavior in large-scale network codes.- Recursive piecewise-linear approximation methods for nonlinear networks.- Computational testing of assignment algorithms.- 9. On Establishing a Group for Testing Mathematical Programs.- Panel Discussion.- 10. Appendix.- Conference program.- List of participants.- A model for the performance evaluation in comparative studies.- Remarks on the comparative evaluation of algorithms for mathematical programming problems.- Comments on a testing center.- Systematic approach for comparing the computational speed of unconstrained minimization algorithms.- The evaluation of optimization software for engineering design.