Abstract
In this article we introduce the notions of Kuhn-Tucker and Fritz John pseudoconvex nonlinear programming problems with inequality constraints. We derive several properties of these problems. We prove that the problem with quasiconvex data is (second-order) Kuhn-Tucker pseudoconvex if and only if every (second-order) Kuhn-Tucker stationary point is a global minimizer. We obtain respective results for Fritz John pseudoconvex problems. For the first-order case we consider Fréchet differentiable functions and locally Lipschitz ones, for the second-order case Fréchet and twice directionally differentiable functions.
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Ivanov, V.I. On a theorem due to Crouzeix and Ferland. J Glob Optim 46, 31–47 (2010). https://doi.org/10.1007/s10898-009-9407-1
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DOI: https://doi.org/10.1007/s10898-009-9407-1
Keywords
- Nonsmooth analysis
- Nonsmooth optimization
- Generalized convexity
- KT pseudoconvex problems
- FJ pseudoconvex problems
- Quasiconvex programming