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Second order necessary and sufficient conditions for convex composite NDO. (English) Zbl 0641.49013
The author studies the problem of minimizing functions of the form \(F:=h\circ f\) where \(h: {\mathbb{R}}^ m\to {\mathbb{R}}\) is a finite-valued convex function and \(f: {\mathbb{R}}^ n\to {\mathbb{R}}^ m\) is continuously differentiable. He extends the second-order necessary and sufficient optimality conditions obtained by A. D. Ioffe [SIAM J. Control Optimization 17, 266-288 (1979; Zbl 0417.49029)] for the particular case in which h is sublinear, to arbitrary convex h. A discussion of the second-order regularity conditions is also included.
Reviewer: M.Studniarski

MSC:
49K10 Optimality conditions for free problems in two or more independent variables
26B25 Convexity of real functions of several variables, generalizations
90C25 Convex programming
90C30 Nonlinear programming
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