Optimization with unary functions

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argument. We define problem (1) to be a unary optimization problem, iff(x) take the form ... The geometric programming problem can be written. Po min ... In the late 1800s Gibbs developed a theory showing that the composition of a complex ...
Mathematical Programming 52 (1991) 167-178 North-Holland

167

Optimization with unary functions Garth P. McCormick* The George Washington University, Washington, DC 20052, USA

Ariela Sofer** George Mason University, Fairfax, VA 22030, USA Received 16 October 1988 Revised manuscript received 17 October 1989 Most nonlinear programming problems consist of functions which are sums of unary functions of linear functions. Advantage can be taken of this form to calculate second and higher order derivatives easily and at little cost. Using these, high order optimization techniques such as Halley's method can be utilized to accelerate the rate of convergence to the solution. These higher order derivatives can also be used to compute second order sensitivity information. These techniques are applied to the solution of the classical chemical equilibrium problem.

1. Introduction: Unary optimization Consider the nonlinear optimization problem min

fo(x)

subjectto

f(x)