Two algorithms for integer optimization

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

This manuscript introduces ANTIGONE, Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-p...

Algorithms for Integer Programming

• Unlike linear programming problems, integer programming problems are very difficult to solve. In fact, no efficient general algorithm is known for their solution. • Given our inability to solve integer programming problems efficiently, it is natural to ask whether such problems are inherently “hard”. Complexity theory, offers some insight on this question. It provides us with a class of probl...

Algorithms for Two Bottleneck Optimization Problems

Generated the Integer Null Space and Conditions for Determination of an Integer Basis Using the ABS Algorithms

Parallel Algorithms for Integer Factorisation

The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the Rivest-Shamir-Adelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisati...