# Global Optimization for Polynomial Programming Problems Usingm-homogeneous Polynomial Homotopies

1989) Global Optimization for Polynomial Programming Problems Usingm-homogeneous Polynomial Homotopies. Technical Report TR-89-31, Computer Science, Virginia Polytechnic Institute and State University. (

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## Abstract

A polynomial programming problem is a nonlinear programming problem where the objective function, inequality constraints, and equality constraints all consist of polynomial functions. The necessary optimality conditions for such a problem can be formulated as a polynomial system of equations, among whose zeros the global optimum must lie. This note applies the theory of m-homogeneous polynomials in Cartesian product projective spaces and recent homotopy algorithms to significantly reduce the work of a naive homotopy approach to the polynomial system formation of the mecessary optimality conditions. The m-homogeneous approach, providing the global optimum, is practical for small problems. For example, the geometric modeling problem of finding the distance between two polynomial surfaces is a polynomial programming problem. Also discussed is a prototype structural design problem.

Item Type: | Departmental Technical Report |
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Subjects: | Computer Science > Historical Collection(Till Dec 2001) |

ID Code: | 168 |

Deposited By: | User autouser |

Deposited On: | 05 December 2001 |