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Duality in Nonlinear Programming: A Simplified Applications-Oriented Development.

AD709184

Publication Date	1970
Personal Author	Geoffrion, A. M.
Page 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 fixed-point 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 function--the optimal value of a program as a function of perturbations of its right-hand side. The approach gives useful geometric and mathematical insights and is closely interwoven with optimality theory. (Author)
Keywords	Nonlinear programming Theorems Perturbation theory Linear programming Quadratic programming Optimization Duality theory
NTIS Subject Category	72E - Operations Research
Corporate Authors	Rand Corp Santa Monica Calif
Document Type	Technical Report
NTIS Issue Number	197018
Contract Number	F44620-67-C-0045

Duality in Nonlinear Programming: A Simplified Applications-Oriented Development.

Duality in Nonlinear Programming: A Simplified Applications-Oriented Development.
AD709184

Publication Date	1970
Personal Author	Geoffrion, A. M.
Page 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 fixed-point 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 function--the optimal value of a program as a function of perturbations of its right-hand side. The approach gives useful geometric and mathematical insights and is closely interwoven with optimality theory. (Author)
Keywords	Nonlinear programming Theorems Perturbation theory Linear programming Quadratic programming Optimization Duality theory
NTIS Subject Category	72E - Operations Research
Corporate Authors	Rand Corp Santa Monica Calif
Document Type	Technical Report
NTIS Issue Number	197018
Contract Number	F44620-67-C-0045