Econometrica: May 1972, Volume 40, Issue 3

A Nonlinear Duality Theorem Without Convexity

https://doi.org/0012-9682(197205)40:3<487:ANDTWC>2.0.CO;2-H
p. 487-496

F. J. Gould, J. P. Evans

Duality in nonlinear programming is investigated via the usual Lagrangian function in the absence of assumptions concerning convexity or differentiability of the underlying functions. Equivalent forms of the primal and dual problems are discussed along with relations between the respective optimal values. A theorem is presented which gives a weak sufficient condition for equality of primal and dual optimal values. Geometric and economic implications of these results are explored.

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