Convex Optimization · Problem 4.37

Duality — Boyd & Vandenberghe

Mathematics — Optimization · generalized-geometric-program

Problem

A generalized geometric program (GGP) is an optimization problem of the form minimizeh0(x)subject tohi(x)≤1,i=1,…,mgi(x)=1,i=1,…,p,(4.70)\begin{array}{ll} \text{minimize} & h_0(x) \\ \text{subject to} & h_i(x) \leq 1, \quad i = 1, \ldots, m \\ & g_i(x) = 1, \quad i = 1, \ldots, p, \end{array} \tag{4.70} where g1,…,gpg_1, \ldots, g_p are monomials, and h0,…,hmh_0, \ldots, h_m are generalized posynomials. Show how to express this generalized geometric program as an equivalent geometric program. Explain any new variables you introduce, and explain how your GP is equivalent to the GGP (4.70).

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