Relaxation Methods for Pure and Mixed Integer Programming Problems

General Solution Methods for Mixed Integer Quadratic Programming and Derivative Free Mixed Integer Non-Linear Programming Problems

In a number of situations the derivative of the objective function of an optimization 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 conve...

Chvátal Closures for mixed Integer Programming Problems

Chvfital introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedron P and integral vector...

Solving Mixed-Integer Programming Problems Using Piecewise Linearization Methods

We present an overview on piecewise linearization methods for MINLPs. This will include the concept of disjunctive constraints, which is necessary to define logarithmic reformulations of the so called disaggregated convex combination method and the convex combination method. For the case of a general univariate quadratic function we also calculate the linearization error and proof that equidist...

Sufficient global optimality conditions for general mixed integer nonlinear programming problems

‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Deterministic Methods for Mixed Integer Nonlinear Programming