
Accession Number : AD0709184
Title : DUALITY IN NONLINEAR PROGRAMMING: A SIMPLIFIED APPLICATIONSORIENTED DEVELOPMENT,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Geoffrion,A. M.
Report Date : JUN 1970
Pagination or Media Count : 82
Abstract : A simpler, more versatile, and more general approach is presented to the computational solution of complex practical optimization problems of nonlinear programming through their duals. Duality theory gives 'prices' for scarce resources, and certain planning problems are more easily solved by passing to an equivalent dual problem. However, the number of applications so far is small compared to the number of theoretical papers. This study avoids differential calculus, minimax theory, and the conjugate functions or fixedpoint theorems employed by most studies in duality theory. Instead, it uses only assumptions that are likely to be verifiable, and relies on the relatively elementary theory of convexity and the concept of a perturbation functionthe optimal value of a program as a function of perturbations of its righthand side. The approach gives useful geometric and mathematical insights and is closely interwoven with optimality theory. (Author)
Descriptors : (*NONLINEAR PROGRAMMING, THEOREMS), PERTURBATION THEORY, LINEAR PROGRAMMING, QUADRATIC PROGRAMMING, OPTIMIZATION
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE