Abstract
In this Chapter, special function classes are studied. First, geodesic (strictly) quasiconvex, geodesic (strictly) pseudoconvex and the difference of two geodesic convex functions are introduced, then convex transformable functions, involving range and domain transformations as well, are treated. These results were mainly published in Rapcsák (1994). In the last section, the structure of smooth pseudolinear functions is characterized, i.e., the explicit formulation of the gradients of smooth pseudolinear functions is given (Rapcsák, 1991). In the next Chapter, it will be shown that this result is the solution of Fenchel problem of level sets in a special case.
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© 1997 Springer Science+Business Media Dordrecht
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Rapcsák, T. (1997). Special Function Classes. In: Smooth Nonlinear Optimization in R n . Nonconvex Optimization and Its Applications, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6357-0_13
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DOI: https://doi.org/10.1007/978-1-4615-6357-0_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7920-1
Online ISBN: 978-1-4615-6357-0
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