Generalized geometric programming with both equality and inequality constraints

Abstract

Abstract This paper suggests a solution of generalized geometric programming with equality constraints by means of an approximation program formed from the primal program by direct algebraic transformation and with a penalty function on the primal objective function. An algorithm was specifically developed to deal with generalized geometric programming problems having both equality and inequality constraints. Kuhn‐Tucker necessary (and sometimes sufficient) conditions for optimality are obtained without increasing too much the degrees of difficulty in the problem. Using a condensation technique introduced by Duffin, it is shown that the approximation program can be solved via a sequence of prototype geometric programming or linear programming codes. A theoretical justification is proved by means of the Kuhn‐Tucker theorem, the condensation properties, and the generalized penalty function concept.