Approximations of a quadratic programming problem with incomplete information
Thesis DisciplineOperations Research
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis deals with the effectiveness of various decision rules derived to approximate the objective function of a quadratic programme. The assumption of the study is that the constraint set of the QP is known precisely but the objective function is known only from the data of various observations made of that function. Various decision rules, some linear and some non-linear, are used to derive from the data objective functions to approximate the true but unknown function. A series of problems are generated to test the effectiveness of these decision rules. The problems are stratified according to the nature of the true quadratic function and the size of the problem in terms of the number of constraints and variables. In addition to comparing the decision rules with each other the study also considers the effects of the type of quadratic function (matrix type), the size of the problem, the number of observations, the scatter pattern of the observations and the curvature (degree of nonlinearity) of the quadratic. In general the decision rules do not behave well except when the curvature is very slight. In most other cases the nonlinear decision rules give much the best results and particularly if the observations are scattered close to the true contrained optimum. The overall conclusion is that it is well worth the effort to obtain an accurate statement of the true objective function unless the function is known to be only slightly nonlinear.