Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 1972, Volume 40, Issue 3

A Nonlinear Duality Theorem Without Convexity<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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