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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.open.diag.uniroma1.it
DTSTAMP:20260409T010144Z
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:http://www.open.diag.uniroma1.it/node/13054
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