Abstract:These finite nearly-linear systems consist of general linear equations and/or linear inequalities, as well as special non-linear relations of the type
    f(x, y) = 0, or f(x, y) £ 0, or f(x, y) ³ 0,
where
    f(x, y) = log [exp (x) + exp (y)]
-- an elementary logarithmic bi-variate function that is convex, “nearly-linear”, and essentially separable into the two simple exponential functions exp (x) and exp (y). This reduction methodology can also be used on general algebraic optimization problems (actually in more than one way), and is a natural extension of the (algebraic) geometric programming reformulations developed during the 1960s and early 1970s by Duffin, Peterson, and Zener. Finally, by virtue of the Stone-Weirstrause approximation theorem, these reformulations can also be used in an approximate way to similarly transform both general continuous systems and general continuous optimization problems that are defined over compact domains -- an indication of the potential importance of any future developments of both algorithms and software (preferably by individuals much younger or more energetic than the author) for numerically solving finite “nearly-linear systems”.