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Zbl 0985.49012
Huang, Liren; Ng, K.F.
Second-order optimality conditions for minimizing a max-function. (English)
[J] Sci. China, Ser. A 43, No.7, 722-733 (2000). ISSN 1006-9283; ISSN 1862-2763/e

The authors consider the problem of minimizing the function $h(x):=\max\{f(x,\tau)\mid \tau \in T\}$, where $x\in R^{p}$, $T$ is a compact metric space and the function $f(\cdot ,\tau)$ is $C^{2}$. Second-order necessary optimality conditions are obtained by using second-order directional derivatives of Chaney and Ben-Tal/Zowe of $h$. These conditions improve an earlier result of {\it H. Kawasaki} [Appl. Math. Optimization 26, No. 2, 195-220 (1992; Zbl 0777.90058)].
[M.Studniarski (Łódź)]

MSC 2000:: *49K35 Minimax problems (necessity and sufficiency)
49J52 Nonsmooth analysis (other weak concepts of optimality)
90C47 Minimax problems

Keywords: max-function; sup-type function; second-order optimality condition; nonsmooth optimization

Citations: Zbl 0777.90058

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