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DTSTART:20171029T030000
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RDATE:20181028T030000
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DTSTART:20180325T020000
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UID:calendar.13054.field_data.0@www.diag.uniroma1.it
DTSTAMP:20230202T152604Z
CREATED:20180328T170137Z
DESCRIPTION:11:30 - A feasible rounding approach for mixed-integer optimiza
tion problemsChristoph NeumannInstitute of Operations Research\, Karlsruhe
Institute of Technology (KIT)Email: christoph.neumann@kit.eduWe introduce
granularity as a sufficient condition for the consistency of a mixed-inte
ger optimization problem\, and show how to exploit it for the computation
of feasible points: for optimization problems which are granular\, solving
certain linear problems and rounding their optimal points always leads to
feasible points of the original mixed-integer problem. Thus\, the resulti
ng feasible rounding approach is deterministic and even efficient\, i.e.\,
it computes feasible points in polynomial time.The optimization problems
appearing in the feasible rounding approaches have a structure that is sim
ilar to that of the continuous relaxation\, and thus our approach has sign
ificant advantages over heuristics\, as long as the problem is granular. F
or instance\, the computational cost of our approach always corresponds to
merely a single step of the feasibility pump. A computational study on op
timization problems from the MIPLIB libraries demonstrates that granularit
y may be expected in various real world applications. Moreover\, a compari
son with Gurobi indicates that state of the art software does not always e
xploit granularity. Hence\, our algorithms do not only possess a worst-cas
e complexity advantage\, but can also improve the CPU time needed to solve
problems from practice.Joint work with: Oliver Stein and Nathan Sudermann
-Merx 12:15 - The Cone Condition and Nonsmoothness in Linear Generalized N
ash GamesOliver SteinInstitute of Operations Research\, Karlsruhe Institut
e of Technology (KIT)Email: stein@kit.eduThe reformulation of a linear gen
eralized Nash game as a single optimization problem by a Nikaido Isoda bas
ed gap function yields a piecewise linear problem. We introduce the so-cal
led cone condition to characterize the differentiability points of this ga
p function. Other regularity conditions such as the linear independence co
nstraint qualification or the strict Mangasarian-Fromovitz condition are o
nly sufficient for smoothness\, but can be verified more easily than the c
one condition. Therefore\, we present special cases where these conditions
are not only sufficient\, but also necessary for smoothness of the gap fu
nction. Our main tool in the analysis is a global extension of the gap fun
ction that allows us to overcome the common difficulty that its domain may
not cover the whole space.Joint work with: Nathan Sudermann-Merx Bio sket
chProfessor Dr. Oliver Stein is the executive director of the Institute of
Operations Research (IOR) in the Karlsruhe Institute of Technology (KIT).
Currently\, he is Editor-in-chief of the international journal Mathematic
al Methods of Operations Research.Prof. Dr. Stein is a renowned scholar wh
ose research interests encompass many topics in Mathematical programming i
ncluding Nonlinear optimization\, Semi-infinite programming\, Nash games\,
Parametric optimization and Mixed integer nonlinear programming. It is im
possible here to even summarize the huge amount of influential works that
he has authored during the last couple of decades.M. Sc. Christoph Neumann
is a Ph.D. student in Continuous Optimization\, Institute of Operations R
esearch (IOR)\, Karlsruhe Institute of Technology (KIT)
DTSTART;TZID=Europe/Paris:20180404T113000
DTEND;TZID=Europe/Paris:20180404T113000
LAST-MODIFIED:20191008T082902Z
LOCATION:Aula Magna DIAG\, VIA ARIOSTO\, 25 Roma
SUMMARY:MORE@DIAG Seminars: (11:30) A feasible rounding approach for mixed-
integer optimization problems\; (12:15) The Cone Condition and Nonsmoothne
ss in Linear Generalized Nash Games - Prof. Dr. Oliver Stein & M. Sc. Chri
stoph Neumann
URL;TYPE=URI:https://www.diag.uniroma1.it/node/13054
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