Accession Number : ADA117994

Title :   Optimal Value Bounds and Posynomial Geometric Programs.

Descriptive Note : Scientific rept.,


Personal Author(s) : Kyparisis,Jerzy

PDF Url : ADA117994

Report Date : 30 Apr 1982

Pagination or Media Count : 39

Abstract : The idea of bounds on the optimal value of a geometric programming problem has been present since the inception of geometric programming (Duffin, Peterson, and Zener), and has proved to be fruitful in applications of GP. The bounds are the immediate consequences of GP duality theory. Recently, this idea has been extended to parametric bounds on the optimal value function f*. Woolsey and Dembo derive a lower bound on f* using the known fact that the dual objective function at a fixed dual-feasible point underestimates f* for all values of certain coefficients (parameters). Fiacco proposed a general approach for calculating upper and lower bounds on f* (particularly simple whenever f* is convex or concave), which utilizes sensitivity information as well as Wolfe's duality theory. This paper is based on similar ideas, except that GP duality theory is used instead of Wolfe's duality and the special structure of GP primal and dual problems is exploited. Several classes of perturbed GP problems are shown to possess convex or concave f*, or at least 'tight' overestimating and underestimating problems with convex or concave optimal values. (Author)

Descriptors :   *Boundary value problems, *Mathematical programming, Parametric analysis, Optimization, Nonlinear programming, Inequalities

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE