Study On Theory Algorithm Of Generalized Geometric Programming

Optimization theory and methods, a new independent subject was formed, in 1947 when Dantzig proposed the solution of general linear programming problem by simplex method. As an important branch of optimization theory, nonlinear programming has always been research field which was universal concerned by various disciplines since the 1960s. As a branch of nonlinear programming, geometric programming theory and algorithms attracted a widespread attention from emerging.The main reasons are: Firstly, the superiority of this method is converted nonlinear programming problem which has nonlinear constrains into the problem of linear equations, at least it can be converted as nonlinear programming problem which has linear equality constraints; Secondly, the objective function and constraints of geometric programming are all for generalized multivariable polynomials, that is ,the form of the algebraic sum of the product of the power of variables. Thirdly,its applications involve almost all links in operation practice and social life. Especially many optimization models which are often epurated from the produce and design of engineering are geometric programming forms. Geometric programming theory and algorithms is a powerful theoretical weapon to explore and solve many complicated problems in operation practice and social life. So, if we can find some simple and cushy efficient algorithm of this special programming, it will produce important theoretical significance and applied value for studying on geometric programming.The main contents in this paper may be inductived in two aspects as follows:1. According to unconstrained generalized geometric programming problem, we present linear auxiliary function by linear conversion technology so that unconstrained generalized geometric programming problem can be transformed into one column convex programming problem. Based on the properties of unconstrained generalized geometric programming and convex programming, we can use the solution of convex programming problem to approach the solution of uncons trained generalized geometric programming problem so that we obtain a new linearization relaxation method which has global convergence. 2. According to polynomial constraint generalized geometric programming problem, by using the First Order Taylor Series Expansion of multivariate function, it will be transformed into linear function.Then we use the solution of transformation convex programming problem to approach the solution of polynomial constraint generalized geometric programming problem. Based on the properties of polynomial constraint generalized geometric programming and convex programming, we present a new algorithm and prove its convergence has been proved.