Abstract
The main goal of this paper is to introduce two generalized convexity notions, to examine their properties and their use in optimization theory, in particular, to deduce necessary and sufficient first order conditions.
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Notes
The original two-place Rosenbrock function is the following \(f(x,y):=100(y-x^2)^2+(1-x)^2\) (see [18]), which is a well-known test function in numerical optimization.
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Acknowledgments
This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP-4.2.4.A/ 2-11/1-2012-0001 “National Excellence Program” and by the Hungarian Research Fund (OTKA) (Grant No.: NK81402).
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Burai, P. Convexity with respect to families of sections and lines and their application in optimization. J Glob Optim 64, 649–662 (2016). https://doi.org/10.1007/s10898-015-0327-y
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DOI: https://doi.org/10.1007/s10898-015-0327-y
Keywords
- Generalized convexity in optimization
- Optimality conditions
- Generalized directional derivative
- Characterization of generalized convexity