Lexicographic geometric programming

The paper presents the Kuhn-Tucker conditions and the duality theory for the lexicographic minimization problem: lex min{F(x)•x∈Rn,G(x)∈0m∈ where F and G are vector valued functions from Rn∈Rs and Rn∈Rm, respectively. The lexicographic duality is then applied for problems with posynomials in the objectives and in the constraints. The duality theory for lexicographic geometric programming is developed and illustrated by a numerical example.