What is Set Optimization, and what you can do with it
A hacking day of Mathematics for Data Science at the Department of Mathematics

Bio
PhD in 1996 and German "Habilitation" in 2005, both in Mathematics, at Martin Luther University HalleWittenberg, Germany. Taught math and math related courses at University HalleWittenberg (Germany), IMPA, Rio de Janeiro (Brazil), Princeton University (USA) and Yeshiva University New York (USA), among them one of the first ever courses on "Convex Analysis and Financial Risk Measures" in 2003. Codeveloped new area "Set Optimization" with surprising applications in mathematical finance, economics, statistics, game theory and multicriteria decision making; invented set optimization approach to risk measures for multivariate positions and to multivariate quantiles. These are two links with more information:Syllabus
Many relatively straightforward mathematical concepts become questionable or even dubious when naively transferred from the realvalued to the multicriteria case, i.e., to more than one objective function. A few examples: (1) What can you say about linear programming duality for multicriteria problems? (ask your OR/optimization prof) (2) What is the quantile, e.g., the median, of a multivariate random variable? (ask your statistics prof) (3) Do the worstcase and bestresponse strategies for twoperson zerosum games still coincide if the payoff is not one, but higher dimensional? (ask your game theory prof) (4) How do you do multiutility maximization, i.e., find best elements for a nontotal preference relation which can only be represented by a (maybe infinite) family of realvalued functions and not a single one? (ask you econ profs) (5) A little more technical, but very fundamental: what is the LegendreFenchel transform/conjugate of a vector or even setvalued function? (ask your physics/calculus of variations/analysis prof) In this lecture, it is shown that the socalled completelattice approach to set optimization (yes, we start with some basics from order and lattice theory) provides new and exiting answers to the above and many more questions in a very textbooklike manner.
References
 A survey: Hamel AH, Heyde F, Loehne A, Rudloff B, Schrage C, Set optimizationa rather short introduction. In: Hamel, A.H., Heyde, F., Loehne, A., Rudloff, B., Schrage, C. (eds.), Set optimization and applications  the state of the art. From set relations to setvalued risk measures, SpringerVerlag Berlin 2015, pp. 65141
 Game theory: A.H. Hamel, A. Loehne, A set optimization approach to zerosum matrix games with multidimensional payoffs, Math. Methods Oper. Res., 88(3), 69397, 2018
 Multiutility maximization: A.H. Hamel, Q.Q. Wang, A set optimisation approach to utility maximisation under transaction costs, Decisions in Economics and Finance 40(12), 257275, 2017
 Statistics: A.H. Hamel, D. Kostner, Cone distribution functions and quantiles for multivariate random variables, J. Multivariate Analysis 167, 97113, 2018
 Multivariate risk measures: A.H. Hamel, F. Heyde, Duality for setvalued measures of risk, SIAM J Financial Math. 1(1), 6695, 2010
 Convex analysis for setvalued functions: A.H. Hamel, A duality theory for setvalued functions I: Fenchel conjugation theory, SetValued Variational Analysis 17(2), 153182, 2009
Schedule
 21 February 2020, 14:3018:30 @ A224 Povo 1
Details
 Poster: PDF
 The participation is free. Please send an email to Prof. Claudio Agostinelli.
 For further information, please contact Prof. Claudio Agostinelli
 Venue: Polo Scientifico e Tecnologico F. Ferrari
 Language: English
 The photo of Andreas Hamel is courtesy by the press office of Free University of BozenBolzano