The Construction of Test Problems

Abstract

Any development or comparison of nonlinear programming software has to be based on extensive numerical tests. These depend on test problems of the form (1), implemented in an appropriate way, about whose mathematical structure as much as possible is known. Most test problems used in the past to test and compare optimization programs consist of so called ‘real life’ problems which are believed to reflect typical structures of practical nonlinear programming problems, for example the Colville [CO 1968] problems, cf. Himmelblau [HI 1972] or Hock, Schittkowski [HS 1980]. But this class of test examples has some severe disadvantages especially since their precise solution is not a priori known so that the efficiency of a code cannot be related to the achieved accuracy. In this chapter, a completely different approach is presented: The construction of randomly generated test problems with predetermined solutions.