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Random projections in mathematical programming

Martedì 7 gennaio 2020 ore 10.30
Sala Consiglio (8° piano)
Dipartimento di Informatica "Giovanni degli Antoni"
(Via Celoria 18 - Milano)

Leo Liberti CNRS - Laboratoire d’Informatique de l’Ecole Polytechnique de Paris (LIX)

Responsabile: Roberto Cordone

Abstract

In the algorithmic trade-off between generality and efficiency, sometimes the only way out is to accept approximate methods. We shall discuss a set of approximating reformulations to various classes of mathematical programming problems, based on random projections. These are a dimensionality reduction methodology for reducing the dimensionality of a set of vectors, so that the lower-dimensional set is approximately congruent to the original one with high probability. The probability of failure falls exponentially  fast as the dimension increases, making this a truly "big data" methodology.
We shall show how to apply this methodology to Linear and Conic Programming, as well as (bounded) Quadratic Programming, and discuss some applications to quantile regression and the basis pursuit LP in compressed sensing.

Short Bio

Leo Liberti obtained his Ph.D. in Global Optimization at mperial College London, held postdoctoral fellowships at Politecnico di Milano and Ecole Polytechnique in France, where he became professor and vice-president of his department.
After two years as a Research Staff Member at IBM Research in New York, he was recruited by CNRS as a Research Director and by Ecole Polytechnique as a part-time professor. His main research interests are mathematical programming with applications to industrial problems, optimization algorithms, 0and distance geometry.
He was awarded the IFORS Distinguished Lectureship in 2018.

 

Martedì 7 gennaio 2020 ore 10.30
Sala Consiglio (8° piano)
Dipartimento di Informatica "Giovanni degli Antoni"
(Via
Celoria 18 - Milano)

Leo Liberti
CNRS - Laboratoire d’Informatique de l’Ecole Polytechnique de Paris (LIX)


Titolo: Random projections in mathematical programming

Abstract: In the algorithmic trade-off between generality and efficiency,
sometimes the only way out is to accept approximate methods.
We shall discuss a set of approximating reformulations to various classes
of mathematical programming problems, based on random projections.
These are a dimensionality reduction methodology for reducing
the dimensionality of a set of vectors, so that the lower-dimensional set
is approximately congruent to the original one with high probability.
The probability of failure falls exponentially fast as the dimension increases, making this a truly "big data" methodology.
We shall show how to apply this methodology to Linear and Conic Programming,
as well as (bounded) Quadratic Programming, and discuss some applications
to quantile regression and the basis pursuit LP in compressed sensing.

Bio:
Leo Liberti obtained his Ph.D. in Global Optimization at Imperial College London,
held postdoctoral fellowships at Politecnico di Milano and Ecole Polytechnique
in France, where he became professor and vice-president of his department.
After two years as a Research Staff Member at IBM Research in New York,
he was recruited by CNRS as a Research Director and by Ecole Polytechnique
as a part-time professor. His main research interests are mathematical
programming with applications to industrial problems, optimization algorithms,
and distance geometry.
He was awarded the IFORS Distinguished Lectureship in 2018.

Responsabile: Roberto Cordone

18 dicembre 2019
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