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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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