Abstract
In this note we correct and improve a zero duality gap result in extended monotropic programming given by Bertsekas (J. Optim. Theory Appl. 139:209–225, 2008).
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Bertsekas, D.P.: Extended monotropic programming and duality. J. Optim. Theory Appl. 139, 209–225 (2008)
Rockafellar, R.T.: Monotropic programming: descent algorithms and duality. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M. (eds.) Nonlinear Programming, vol. 4, pp. 327–366. Academic Press, San Diego (1981)
Rockafellar, R.T.: Network Flows and Monotropic Optimization. Wiley, New York (1984). Republished by Athena Scientific, Belmont (1998)
Zălinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)
Boţ, R.I., Wanka, G.: A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. Nonlinear Anal. 64, 2787–2804 (2006)
Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976)
Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Hiriart-Urruty, J.-B., Phelps, R.R.: Subdifferential calculus using ε-subdifferentials. J. Funct. Anal. 118, 54–166 (1993)
Hantoute, A., López, M.A., Zălinescu, C.: Subdifferential calculus rules in convex analysis: a unifying approach via pointwise supremum functions. SIAM J. Optim. 19, 863–882 (2008)
Dinh, N., López, M.A., Volle, M.: Functional inequalities in the absence of convexity and lower semicontinuity with applications to optimization. Preprint available at http://www.eio.ua.es/busqueda/publicacion.asp?p=1&c=10 (2009)
López, M.A., Volle, M.: On the subdifferential of the supremum of an arbitrary family of extended real-valued functions. Preprint available at http://www.eio.ua.es/busqueda/publicacion.asp?sp=1&c=10 (2009)
Fang, D.H., Li, C., Ng, K.F.: Constraint qualifications for extended Farkas’s lemmas and Lagrangian dualities in convex infinite programming. SIAM J. Optim. 20, 1311–1332 (2009)
Li, C., Fang, D., López, G., López, M.A.: Stable and total Fenchel duality for convex optimization problems in locally convex spaces. SIAM J. Optim. 20, 1032–1051 (2009)
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Communicated by J.-C. Yao.
The authors are grateful to an anonymous reviewer for his/her remarks.
Research of R.I. Boţ was partially supported by DFG (German Research Foundation), project WA 922/1-3.
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Boţ, R.I., Csetnek, E.R. On a Zero Duality Gap Result in Extended Monotropic Programming. J Optim Theory Appl 147, 473–482 (2010). https://doi.org/10.1007/s10957-010-9733-y
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DOI: https://doi.org/10.1007/s10957-010-9733-y