zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Constrained optimality conditions in terms of proper and adjoint exhausters. (English) Zbl 1209.90349
Summary: The notions of exhaustive families of upper convex and lower concave approximations (in the sense of B.N. Pschenichnyi) were introduced by A.M. Rubinov. For some classes of nonsmooth functions, these tools appeared to be very productive and constructive (e.g., in the case of quasidifferentiable functions). Dual tools the upper exhauster and the lower exhauster can be employed to describe optimality conditions and to find directions of steepest ascent and descent. If a proper exhauster is known (for minimality conditions we need an upper exhauster, while for maximality ones a lower exhauster is required), the above problems are reduced to the problems of finding the nearest points to convex sets. If we study, e.g., the minimization problem and a lower exhauster is available, it is required to convert it into an upper one. It has been shown earlier how to use a lower (upper) exhauster to get conditions for a minimum (maximium) without converting the lower (upper) exhauster into an upper (lower) one in the unconstrained case. In the present paper the constrained case is described in details.
90C46Optimality conditions, duality
90C30Nonlinear programming
49J52Nonsmooth analysis (other weak concepts of optimality)