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)
Strict efficiency in vector optimization. (English) Zbl 1010.90075

The author extends the notion of strict minimum for scalar optimization problems to vector optimization problems. The notion of strict local minimum of order m and strict local minimum for vector optimization problems are introduced. Their properties and characterization are studied for multiobjective problems. Also the notion of super-strict efficiency for multiobjective problems is introduced and it is shown that these notions coincide in the scalar case. The necessary conditions for strict and super-strict minimality of order m for a multiobjective problem are stated by making use of the directional derivatives already considered by M. Studniarski [SIAM J. Control Optim. 24, 1044–1049 (1986; Zbl 0604.49017)] and M. Studniarski [SIAM J. Control Optim. 24, 1044–1049 (1986; Zbl 0604.49017)] and D. E. Ward [J. Optim. Theory Appl. 80, No. 3, 551–571 (1994; Zbl 0797.90101)].

A necessary and sufficient condition for strict efficiency of order 1 for Hadamard differentiable functions is established followed by a characterization of super-strict efficiency of order 1 for Fréchet differentiable functions. The author claims that this extends to multiobjective problems th sufficient optimality conditions given in Theorem 6.3 of chapter 4 by M. R. Hestenes [Optimization Theory: The Finite Dimensional Case, Wiley, New York (1975; Zbl 0327.90015), Krieger, Huntington (1981)].

Reviewer: R.N.Kaul (Delhi)

MSC:
90C29Multi-objective programming; goal programming
90C46Optimality conditions, duality