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)
Lexicographical order and duality in multiobjective programming. (English) Zbl 0646.90076
Developed is a duality theory in multiple objective convex programming theory by using a lexicographical approach. The motivation of this is in extending some known results to problems which do not meet some regularity assumptions. The usual scalarization had to be replaced by nonnegative linear combinations with vector coefficients of the objectives, which permits to obtain all the Pareto minima. It should be noted that the methods employed in this paper could perhaps be applied in connection with other duality theories in multiobjective programming.
Reviewer: M.Todorov

MSC:
90C31Sensitivity, stability, parametric optimization
90C25Convex programming
49N15Duality theory (optimization)
WorldCat.org
Full Text: DOI
References:
[1] Arrow, K. J.; Barankin, E. W.; Blackwell, D.: Admissible points of convex sets. Contribution to the theory of games, 87-91 (1953) · Zbl 0050.14203
[2] Brunelle, S.: Duality for multiple objective convex programs. Mathematics of operations research 6, 159-172 (1981) · Zbl 0497.90068
[3] Di Guglielmo, F.: Nonconvex duality in multiobjective optimization. Mathematics of operations research 2, 285-291 (1977) · Zbl 0406.90068
[4] Gros, C.: Generalization of Fenchel’s duality theorem for convex vector optimization. European journal of operational research 2, 368-376 (1978) · Zbl 0424.90068
[5] Isermann, H.: On some relations between a dual pair of multiple objective dual programs. Zeitschrift für operations research 22, 33-41 (1978) · Zbl 0375.90049
[6] Jahn, J.: Duality in vector optimization. Mathematical programming 25, 343-353 (1983) · Zbl 0497.90067
[7] Martínez-Legaz, J. E.: Exact quasiconvex conjugation. Zeitschrift für operations research 27, 257-266 (1983) · Zbl 0522.90069
[8] Martínez-Legaz, J. E.: Lexicographical order, inequality systems and optimization. Proceedings of the 11th IFIP conference on system modelling and optimization, 203-212 (1984) · Zbl 0563.90084
[9] Rödder, W.: A generalized saddlepoint theory. European journal of operational research 1, 55-59 (1977) · Zbl 0383.90099
[10] Rosinger, E. E.: Duality and alternative in multiobjective optimization. Proceedings of the American mathematical society 64, 307-312 (1977) · Zbl 0333.49030
[11] Tanino, T.; Sawaragi, Y.: Duality theory in multiobjective programming. Journal of optimization theory and applications 27, 509-529 (1979) · Zbl 0378.90100
[12] Tanino, T.; Sawaragi, Y.: Conjugate maps and duality in multiobjective optimization. Journal of optimization theory and applications 31, 473-499 (1980) · Zbl 0418.90080
[13] Tanino, T.: Saddle points and duality in multi-objective programming. International journal systems science 13, 323-335 (1982) · Zbl 0487.49021