Abstract

In a number of situations the derivative of the objective function of an op-timization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of convergence to local minima are provided for two of the implementations. In the development of the algorithm several other contributions are made. The derivative free algorithm requires the solution of several mixed inte-ger quadratic programming subproblems and novel methods for solving non-convex instances of these problems are developed in this thesis. Additionally, it is shown that the current definitions of local minima for mixed integer pro-