This chapter is devoted to a branch of optimization called geometric programming. It originated in the 1960s and early references are Zener (1961) and Duffin (1962). The term “geometric programming” is actually a misnomer as explained below, but it has stuck. A better term would be “posynomial programming,” since the problems under investigation involve posynomial functions, which we will define below. Our discussion commences with unconstrained geometric programming. Readers may wonder why this was not covered in Chap. 2. As we develop the theory of geometric programming below, we will have to resort to results from duality for nonlinear programming, an issue not covered until Chap. 4. General references are Beightler and Phillips (1976), Eiselt et al. (1987), Avriel (2013), and Bazaraa et al. (2013). An entertaining account can be found in Woolsey and Swanson (1975).
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