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Generalized invexity for nonsmooth vector-valued mappings. (English) Zbl 0679.90071
We define four types of invexity for Lipschitz vector-valued mappings from ${R}^{p}$ to ${R}^{q}$ that generalize previous definitions of invexity in the differentiable setting. After establishing relationships between the various definitions, we show the importance of the concept of nonsmooth invexity in the field of optimization. In particular, we obtain conditions sufficient for optimality in unconstrained and cone- constrained nondifferentiable programming that are weaker than previous conditions presented in the literature; we also obtain weak and strong duality results.
Reviewer: Th.W.Reiland
##### MSC:
 90C31 Sensitivity, stability, parametric optimization 49J52 Nonsmooth analysis (other weak concepts of optimality) 26B25 Convexity and generalizations (several real variables) 54C60 Set-valued maps (general topology) 49N15 Duality theory (optimization)