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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

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