Abstract

Finding the global optimal solution for a general nonlinear program is a difficult task except for very small problems. In this paper we identify a class of nonlinear programming problems called polynomial programming problems (PP). A polynomial program is an optimization problem with a scalar polynomial objective function and a set of polynomial constraints. By using Groebner Bases, we can determine the global minimum of a polynomial program in a reasonable amount of time and memory. 1 Introduction In almost every engineering discipline, the need for optimizing a particular application at hand arises constantly. In engineering applications, global solutions mean the most efficient use of resources under practical constraints. Optimization techniques have been a fruitful domain in engineering research. For linear and quadratic programming problems, efficient algorithms have been developed to guarantee global solutions with convexity. For general nonlinear programs, various optimizatio...

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