Watson, Layne T.Morgan, Alexander P.2013-06-192013-06-191989http://hdl.handle.net/10919/19554A 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.application/pdfenIn CopyrightTechnical reportTR-89-31http://eprints.cs.vt.edu/archive/00000168/01/TR-89-31.pdf