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On second-order sufficient optimality conditions for \(C^{1,1}\)- optimization problems. (English) Zbl 0647.49014

The authors consider the following optimization problem:
minimize \(f_ 0(x)\) subject to \(x\in D\equiv \{x|\) \(f_ i(x)=0\) for \(i\in I_ 1\), \(f_ i(x)\leq 0\) for \(i\in I_ 2\}\), where \(I_ 1\), \(I_ 2\) are finite sets of indices, \(f_ i\) are, for all \(i\in \{0\}\cup I_ 1\cup I_ 2\), differentiable functions having a locally Lipschitzian gradient on an open set \(\Omega\), \(\Omega\subset E\) n.
Second order sufficient optimality conditions are derived, and applications to semi-infinite programming are discussed.
Reviewer: K.Zimmermann

MSC:

49K10 Optimality conditions for free problems in two or more independent variables
90C34 Semi-infinite programming
90C30 Nonlinear programming
90C31 Sensitivity, stability, parametric optimization
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References:

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