# Directed Derivatives of Convex Compact-Valued Mappings

R. Baier, E. Farkhi:
**Directed Derivatives of Convex Compact-Valued Mappings**

in:
*Proceedings of the Conference "Advances in Convex Analysis and Global Optimization: Honoring the Memory of C. Caratheodory (1873-1950)" held at Pythagorion, Samos, Greece in June 5-9, 2000,*
*
N. Hadjisavvas, P. M. Pardalos
(eds.)
*

*Nonconvex Optimization and Its Applications*

**54**, Kluwer Academic Publishers, Dordrecht-Boston-London, 2001, 501 - 514

DOI:
10.1007/978-1-4613-0279-7_32

MR Nummer:
1846174

Zentralblattnummer:
1001.46027

Keywords: directed sets; set-valued derivatives; differences of convex sets and their visualization; affine, semi-affine, quasi-affine maps; embedding of convex compact sets into a vector space; directed intervals

Mathematics Subject Classification Code: 26E25 (52A20 58C25 46G05 54C60 41A45)

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## Abstract:

Convex compact sets can be embedded into the Banach space of directed sets. Directed sets allow a visualization as possibly non-convex, compact sets in |R^n and hence, this space could be used to visualize differences of embedded convex compact sets. The main application is the visualization as well as the theoretical and numerical calculation of set-valued derivatives. Known notions of affine, semi-affine and quasi-affine maps and their derivatives are studied.

## Contents:

1. | Introduction |

2. | Directed Sets |

3. | Derivatives of Set-Valued Mappings |

4. | Examples of Directed Derivatives |

5. | Summary |