Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0647.90076
Rueda, Norma G.; Hanson, Morgan A.
Optimality criteria in mathematical programming involving generalized invexity.
(English)
[J] J. Math. Anal. Appl. 130, No.2, 375-385 (1988). ISSN 0022-247X

Constrained optimization problems of the form (1) minimize f(x) subject to $x\in X\subseteq R\sp n$, g(x)$\le 0$, with differentiable functions f, g f type I or type II are considered: The functions f, g are called of type I with respect to a vector function $\eta$ (x) at $x\sb 0$ if the relations $$f(x)-f(x\sb 0)\ge [\nabla\sb xf(x\sb o)]' \eta (x),\quad - g(x\sb 0)\ge [\nabla\sb xg(x\sb o)] \eta (x)$$ hold for all feasible x of the problem (1). \par Similarly f, g are called of type II with respect to x at $x\sb 0$, if $$f(x\sb 0)-f(x)\ge [\nabla\sb xf(x)]' \eta (x),\quad and\quad -g(x)\ge \nabla\sb xg(x) \eta (x)$$ are satisfied for all feasible solutions of the problem (1). Various sufficient conditions, under which the functions f, g are of type I or II are given. Sufficient optimality conditions for the problem (1), in which f, g are of type I or II are proved.
[K.Zimmermann]
MSC 2000:
*90C30 Nonlinear programming
49K05 Free problems in one independent variable (nec./ suff.)

Keywords: Sufficient optimality conditions

Cited in: Zbl 0914.90239

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences