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Zbl 0679.90071
Reiland, Thomas W.
Generalized invexity for nonsmooth vector-valued mappings. (English)
[J] Numer. Funct. Anal. Optimization 10, No.11-12, 1192-1202 (1989). ISSN 0163-0563; ISSN 1532-2467/e

We define four types of invexity for Lipschitz vector-valued mappings from $R\sp p$ to $R\sp q$ 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.
[Th.W.Reiland]

MSC 2000:: *90C31 Sensitivity, etc.
49J52 Nonsmooth analysis (other weak concepts of optimality)
26B25 Convexity and generalizations (several real variables)
54C60 Set-valued maps
49N15 Duality theory (optimization)

Keywords: Lipschitz vector-valued mappings; nonsmooth invexity; cone-constrained nondifferentiable programming; weak and strong duality results; nonsmooth mapping; generalized gradient; generalized Jacobian; optimality conditions

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