zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On a zero duality gap result in extended monotropic programming. (English) Zbl 1229.90264
Authors’ abstract: “In this note we correct and improve a zero duality gap result in extended monotropic programming given by D. P. Bertsekes [ J. Optim. Theory Appl. 139, No. 2, 209–225 (2008; Zbl 1163.90015)].”
MSC:
90C48Programming in abstract spaces
90C46Optimality conditions, duality
References:
[1]Bertsekas, D.P.: Extended monotropic programming and duality. J. Optim. Theory Appl. 139, 209–225 (2008) · Zbl 1163.90015 · doi:10.1007/s10957-008-9393-3
[2]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)
[3]Rockafellar, R.T.: Network Flows and Monotropic Optimization. Wiley, New York (1984). Republished by Athena Scientific, Belmont (1998)
[4]Zălinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)
[5]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) · Zbl 1087.49026 · doi:10.1016/j.na.2005.09.017
[6]Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976)
[7]Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
[8]Hiriart-Urruty, J.-B., Phelps, R.R.: Subdifferential calculus using ϵ-subdifferentials. J. Funct. Anal. 118, 54–166 (1993)
[9]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) · Zbl 1163.49014 · doi:10.1137/070700413
[10]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)
[11]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)
[12]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) · Zbl 1206.90198 · doi:10.1137/080739124
[13]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) · Zbl 1189.49051 · doi:10.1137/080734352