A New Introduction to Global Optimization over Polyhedrons

For some kinds of linearly constrained optimization problems with unique optimal solution, such as linear and convex problems, the single local optimum is also global. However, there are a broad variety of problems in which the property of unique solution cannot be simply postulated or verified. The paper presents an effective approach for the global linearly constrained optimization problem with continuous objective function. With the help of a parametric representation of the feasible region an equivalent unconstrained problem is constructed which is much easier to solve. Our aim is to propose a new introduction to global optimization, the design of a general solution algorithm that always finds the solution and provides useful information such as bounding of the objective function. The algorithm and its applications are presented in the context of a numerical example. Key-Words: Global optimization, Linearly constrained optimization, Tight bounding, Nonlinear programming, Polyhedrons, Mathematical programming