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Nondifferentiable (Φ,ρ)-type I and generalized (Φ,ρ)-type I functions in nonsmooth vector optimization
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Tadeusz Antczak
Published/Copyright:
October 19, 2013
Abstract.
In this paper, new classes of nondifferentiable generalized invex functions are introduced. Further, nonsmooth vector optimization problems with functions belonging to the introduced classes of (generalized) (Φ,ρ)-type I functions are considered. Sufficient optimality conditions and duality results for such classes of nonsmooth vector optimization problems are established. It turns out that the presented results are proved also for such nonconvex vector optimization problems in which not all functions constituting them possess the fundamental property of invexity.
Keywords: Multiobjective programming; nondifferentiable (Φ,ρ)-type I functions; optimality conditions; duality
Received: 2012-01-02
Revised: 2012-11-12
Accepted: 2012-12-20
Published Online: 2013-10-19
Published in Print: 2013-12-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Multiobjective programming;
nondifferentiable (Φ,ρ)-type I functions;
optimality conditions;
duality
Articles in the same Issue
- Masthead
- A characterization of pseudo-Einstein real hypersurfaces of a complex space form
- An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
- Topological conjugation to uniformly piecewise linear transformations
- Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
- An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain
- Nondifferentiable (Φ,ρ)-type I and generalized (Φ,ρ)-type I functions in nonsmooth vector optimization
- An optimal double inequality between logarithmic and generalized logarithmic means
- A further generalization of the 𝒯𝒜d-density topology
- Erratum Bloch varieties of higher-dimensional, periodic Schrödinger operators [J. Appl. Anal. 15 (2009), 33–46]
