Applications of integer relation algorithms

Applications of integer relation algorithms

Let a be a vector of real numbers. By an integer relation for a we mean a non-zero integer vector c such that ca T = 0. We discuss the algorithms for nding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.

Parallel integer relation detection: Techniques and applications

Let {x1, x2, · · · , xn} be a vector of real numbers. An integer relation algorithm is a computational scheme to find the n integers ak, if they exist, such that a1x1 + a2x2 + · · · + anxn = 0. In the past few years, integer relation algorithms have been utilized to discover new results in mathematics and physics. Existing programs for this purpose require very large amounts of computer time, d...

Applications and algorithms for mixed integer nonlinear programming

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear const...

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

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...