Curriculum Vitae

Curriculum Vitae
General Information
Name:
Dr. Carola Schrage
Birthday/place
August 26th, 1978/ Wuppertal
Nationality
German
Home Address:
Via Motta 4
21020 Varano Borghi (VA)
Italy
Telephone:
+39 388 4837 918
E-Mail:
[email protected]
Education since leaving school
2009
Ph.D., Martin Luther Universität Halle Wittenberg,
graded magna cum laude
2005
Diploma (M.S.), Martin Luther Universität Halle Wittenberg,
graded sehr gut
Present appointment
since 11.2013
Research fellow,
Dept. of Economics and Political Sciences, Università della Valle
d'Aosta
Research position under the supervision of G.P. Crespi in the
project Metodi matematici dell'economia e delle scienze attuariali e nanziarie
Professional experience
02.2013 03.2013
Research fellow,
Dept. of Economics and Political Sciences, Università della Valle
d'Aosta
Research position under the supervision of G.P. Crespi in the
project Ottimizzazione: teoria e metodi
12.2012
Adjunct professor,
Dept. of Economics and Political Sciences, Università della Valle
d'Aosta
Teaching of a lecture and exercise class
12.2011
Adjunct professor,
Dept. of Economics and Political Sciences, Università della Valle
d'Aosta
Teaching of a lecture and exercise class
04.2011 09.2011
Adjunct professor,
Faculty of Natural Science II, Martin Luther Universität Halle
Wittenberg
Teaching of two exercise classes
10.2010 03.2011
Adjunct professor,
Faculty of Transportation Science, Technische Universität Dresden
Teaching and supervision of Bachelor thesises,
Visiting positions
04. 05.2013
Dept. of Economics, Università degli Studi dell'Isubria, Varese
11.2012
Institute of Mathematical Sciences, University of Yeshiva
09.2009 02.2010
06.2009 08.2009
Department of Mathematics, Universitat Autònoma de Barcelona
Department of Operations Research and Financial Engineering,
Princeton University
Experience in academic teaching
2012 Lecture: Multivariable Optimization (Bachelor)
Università della Valle d'Aosta;
2011 Lecture: Vector Optimization, a Generalized Approach (Bachelor)
Università
della Valle d'Aosta;
2011 Exercise Course: Nonlinear Optimization (Master)
Martin Luther Universität
Halle Wittenberg;
2011 Exercise Course: Linear Optimization (Bachelor)
Martin Luther Universität
Halle Wittenberg;
2010-2011 Lecture and Exercise Course: Optimization in Logistics Companies (Bachelor)
Technische Universität Dresden;
2010 Tutorial: Actuarial Mathematics (Bachelor)
Martin Luther Universität Halle
Wittenberg
2003 Exercise Course: Theoretical Computer Science
at a VWSummerschool for
high school students, Martin Luther Universität Halle Wittenberg
Other academic responsibilities
Coorganizer and scientic board
II,
Coorganizer
Coorganizer of the conference
I,
Editorial board
of the conference
Set Optimization Meets Finance
Bruneck, September 2014
Set Optimization Meets Finance
Wittenberg, August 2012
of the proceeding Set Optimization and Applications - The State
of the Art - From Set Relations to Set-Valued Risk Measures
Referee for
Journal of Global Optimization
Journal of Optimization Theory and Applications
Optimization
Research Interests
Convex and variational analysis,
Optimization theory,
in particular for vector and setvalued functions
in particular optimality conditions and duality for problems
with setvalued objectives
Application of the above
to setvalued risk measures for markets with transaction
costs
Ordered algebraic structures
like lattice ordered residuated monoids as fundamen-
tals for setvalued variational analysis
Working Papers
Variational principles and optimality in setvalued optimization
A Dini derivative for abstract functions
with G. Crespi
with F. Heyde
Approximate solutions in Set Optimization
with G. Crespi and M.Rocca
Awards & Grants
2005 2006
2005
Ph.D. Grant of the Federal State of SachsenAnhalt
DMV (German Mathematical Association) Award for excellent
diploma
2005
DMV Award for excellent diploma thesis
2005
Georg Cantor Association Award for excellent diploma
Publications
A Minty variational principle for set optimization
with A.H. Hamel and G.P. Crespi,
submitted, 2013
Set optimization meets variational inequalities
with G.P. Crespi, submitted, 2013
Directional derivatives and subdierentials of set-valued convex functions with A.H.
Hamel, Pacic Journal of Optimization accepted for publication,
2013
An algorithm to solve polyhedral convex set optimization problems
Optimization, 62 (1), 131141, 2013
with A. Löhne,
Continuity concepts of set-valued functions and a fundamental duality formula for set-valued
optimization with F. Heyde, Journal of Mathematical Analysis
and Applications, 397 (2) 772784, 2013
Scalar representation and conjugation of setvalued functions, Optimization,
2012,
DOI:10.1080/02331934.2012.741126
Notes about extended real- and set-valued functions with
Convex Analysis, 2 (19) 355384, 2012
Setvalued convex analysis
A.H. Hamel,
Journal of
Ph.D. thesis, MartinLutherUniversity HalleWittenberg,
2009
Algebraische Trennungsaussagen (Algebraic separation theorems)
MartinLutherUniversity
HalleWittenberg, Diploma thesis, 2005
Selected Talks and Conferences
XXXVII AMASES Meeting,
Stresa, September 2013:
Variational inequalities in set optimization
Dipartimento di Economia, Università degli Studi dell'Isubria,
Varese, Febuary 2013:
'SetValued Optimization and Conlinear Structures, invited talk
Institute of Mathematical Sciences, University of Yeshiva,
New York, November 2012:
Variational Inequalities in set optimization, invited talk
ISMP, International Symposium on Mathematical Programming,
Berlin, August 2012:
Dini derivatives for vector and setvalued functions
Set Optimization Meets Finance,
Wittenberg, August 2012:
Minty variational principle for set optimization
Institute of Computer Science, University of Saarbrücken,
January 2012:
A solution concept for multicriteria optimization, invited talk
Dipartimento di Economia, Università degli Studi dell'Isubria,
Varese, December 2011:
A setvalued approach to vector optimization, invited talk
Department of Decicion Science, Bocconi University,
Milano, December 2011:
A setvalued approach to vector optimization, invited talk
ORP3 Euro Conference for Young OR Researchers,
Cadiz, September 2011:
Conjugate duality of setvalued functions
SIAM Optimization Conference,
Darmstadt, May 2011:
Fenchel-Rockafellar duality for set-valued problems via scalarization, invited talk
International Conference on Optimization,
CRM Bellaterra, November 2010:
What's an extended real valued function and how to deal with
it?
Workshop on Vector and Setvalued Optimization,
Residuated binary operators
Languages
German
native
English
uent, C2
Spanish
basic, B1
Italian
basic, A1
Japanese
basic, A1
Varano Borghi, December 19, 2013
Wittenberg, September 2010:
Statement of interest
As junior researcher at the Free University of Bolzano, the applicant aims to
investigate new approaches in vector and set optimization and ways to apply these
theoretical results to nancial market problems.
Set Optimization is a new eld which emerged over the last two decades of the
20th century. In classical extremal problems, the objective function has real numbers
as output (the image space is one dimensional) while if one considers more than one
objective, the problem is called a multicriteria or vector optimization problem.
Multicriteria optimization is the basis of the vast area of Decision Making and can
be traced back to Edgeworth's and Pareto's work at the end of the 19th century.
There are two main motivations for extending the universe from a 'vectorvalued'
to a 'setvalued' one:
The rst one is of mathematical nature.
Many formulas and results in one
dimensional optimization with important applications cannot be established in the
framework of multidimensional optimization. But they can, if one accepts a set
valued setting. This surprising insight is one of the main contributions of the lattice approach, initiated by a group of researchers (Hamel, Heyde, Loehne, Rudlo,
Schrage) formerly working at University Halle-Wittenberg.
As a consequence it
turned out that at times it is better to look at a vector optimization problem from
the setvalued point of view. One instance is the duality theory, where new results
could be discovered and already led to new computational methods, compare e.g.
Löhne and Schrage, 2012.
The second motivation stems from applications in nancial mathematics.
It
turned out that models for nancial markets with frictions (transaction costs, bid
ask price spreads, non-constant interest rates, liquidity and trading constraints etc.)
very naturally lead to optimization problems which are genuinely set-valued. This
seems to be motivation enough to take stock of the development in the eld of setvalued variational analysis and optimization as well as its application to nancial
models, and discuss possible future research areas and questions.
Ultimately, an enormous potential is seen in the application of parallel computers
to set optimization problems. The algorithms for setvalued optimization problems
are perfectly suited for parallel computing, which is expected to lead to signicant
contributions for the computation of real world applications in the above mentioned
classes of problems and beyond.
The major goals for the near future include the characterization of optimality
conditions in terms of variational inequalities, a concept of approximate solutions and
numerical approaches to setvalued optimality problems and ultimately applications
in nancial mathematics will be considered.
Varano Borghi, 18/12/2013