A conjugate duality scheme generating a new class of differentiable duals

SIAM Journal on Optimization

Volumn 6, Issue 3, 1996, Pages 617-625

  Ben Tal, Aharon ^a   Teboulle, Marc ^b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Augmented Lagrangians; Conjugate duality; Convex optimization; Entropic proximal mappings

Indexed keywords

EID: 0030303853     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623493254297     Document Type: Article

References (9)

1. D. BERTSEKAS, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.
2. I. CSISZAR, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar., 2 (1967), pp. 299-318.
3. E. G. GOL'SHTEIN AND N. V. TRET'YAKOV, Modified Lagrangian Functions (Theory and Methods Optimization), Nauka, Moscow, USSR, 1989.
4. J. J. MOREAU, Proximité et dualité dans un espace Hilbertien, Bull. Soc. Math. France, 93 (1965), pp. 273-299.
5. R. A. POLYAK, Modified barrier functions, theory and methods, Math. Programming, 54 (1992), pp. 177-222.
6. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
7. _, A dual approach to solving nonlinear programming problems by unconstrained optimization, Math. Programming, 5 (1973), pp. 354-373.
8. _, Conjugate Duality and Optimization, CBMS, Vol. 16, Society for Industrial and Applied Mathematics Publications, Philadelphia, PA, 1974.
9. M. TEBOULLE, Entropic proximal mappings with application to nonlinear programming, Math. Oper. Res., 17 (1992), pp. 670-690.