Abstract
We give hypotheses, valid in reflexive Banach spaces (such as L p for ∞>p>1 or Hilbert spaces), for a certain modification of the ordinary lagrangean to close the duality gap, in convex programs with (possibly) infinitely many constraint functions.
Our modification of the ordinary lagrangean is to perturb the criterion function by a linear term, and to take the limit of this perturbed lagrangean as the norm of this term goes to zero.
We also review the recent literature on this topic of the “limiting lagrangean”.
Partially supported by grant DAAG29-80-C00317, Army Research Office, Research Triangle Park, North Carolina, U.S.A.
Partially supported by grant ENG7900284 of the National Science Foundation.
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© 1981 The Mathematical Programming Society
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Duffin, R.J., Jeroslow, R.G. (1981). Lagrangean functions and affine minorants. In: König, H., Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach. Mathematical Programming Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120920
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DOI: https://doi.org/10.1007/BFb0120920
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