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DTSTART:20171029T030000
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DTSTART:20170326T020000
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UID:calendar.12417.field_data.0@diag.uniroma1.it
DTSTAMP:20220525T190730Z
CREATED:20170628T105104Z
DESCRIPTION:Titolo: 'A Dual Step for Improving Alternating Augmented Lagran
gian Methods for Semidefinite Programming'Speaker: Marianna De Santis(Joi
nt work with Franz Rendl e Angelika Wiegele)Abstract:'It is well known tha
t SDP problems are solvable in polynomial time by interior point methods (
IPMs). However\, if the number of constraints m in an SDP is of order O(n^
2)\, when the unknown positive semidefinite matrix is n × n\, interior poi
nt methods become impractical both in terms of the time and the amount of
memory required at each iteration. As a matter of fact\, in order to compu
te the search direction\, IPMs need to form the m × m positive definite Sc
hur complement matrix M and find its Cholesky factorization. On the other
hand\, first-order methods typically require much less computation effort
per iteration\, as they do not form or factorize these large dense matrice
s.Furthermore\, some first-order methods are able to take advantage of pro
blem structure such as sparsity. Hence\, they are often more suitable\, an
d sometimes the only practical choice for solving large-scale SDPs.Most ex
isting first-order methods for SDP are based on the augmented Lagrangian m
ethod. Alternating direction augmented Lagrangian (ADAL) methods usually p
erform a projection onto the cone of semidefinite matrices at each iterati
on.With the aim of improving the convergence rate of ADAL methods\, we pro
pose to update the dual variables before the projection step. Numerical re
sults are shown on both random instances and on instances for the computat
ion of the Lovàsz theta number\, giving some insights on the benefits of t
he approach.' Titolo: 'A heuristic method to solve the challenging Sales
Based Integer Program for Network Airlines Revenue Management'Speaker: Gio
rgio Grani(Joint work with Gianmaria Leo\, Laura Palagi\, Mauro Piacentini
\, Hunkar Toyoglu)Abstract:'Revenue Management (RM) has been playing over
recent years an increasingly crucial role in both strategic and tactical d
ecisions of Airlines business. Successful RM processes aim to achieve the
maximization of revenue by leveraging huge amount of data\, upcoming techn
ologies and more sophisticated approaches to measure the RM performances.
Multiple phases of RM processes\, as well as different components of RM sy
stems\, are based on the solution of large integer programming models\, li
ke the well-known Sales Based Integer Program (SBIP)\, whose instances tur
n out to be challenging\, or even not solvable in practice by the state-of
-art MIP solvers.Our work aims to investigate useful polyhedral properties
and introduce a practical heuristic method to find a good solution of har
d instances of SBIP. We use a LP-based branch-and-bound paradigm. Firstly\
, we strengthen the linear relaxations of subproblems by introducing effec
tive Chvátal-Gomory cuts\, exploiting the structure of the polytope.Our ma
in contribution consists in the decomposition of the SBIP into two stage M
INLP smaller problems. The basic idea is to separate the optimal allocatio
n of the capacity to the markets and then to split it among the different
travel options on each market\, differently from the traditional leg-based
decomposition. This leads to the formulation of the market subproblems as
piecewise linear problem. We define a concave approximation of the piecew
ise linear objective function in order to reach a good solution in reasona
ble time. Decomposition ensures a radical reduction of the dimension of th
e problem instances\, both the number of variables and of constraints\, wh
ile the concave approximation reduces computational times for the solution
of each subproblems. Computational results are reported. '
DTSTART;TZID=Europe/Paris:20170727T110000
DTEND;TZID=Europe/Paris:20170727T120000
LAST-MODIFIED:20200515T073055Z
LOCATION:Aula A2 - DIAG
SUMMARY:MORE@DIAG: Marianna De Santis - Giorgio Grani - Marianna De San
tis\, Giorgio Grani\n\n\n \n \n\n \n\n\nMarianna\n\n\nDe Santis \n\n
\n\n \n\n\n\n\n\nProfessore associato\n\n\npagina personale\n\nstanza
: \n\nA120\n\ntelefono: \n\n+390677274078 \n\n \n\n \n\nBiografia: \n
\n\n\n2007: Laurea in Matematica (110 e lode)\, Sapienza Università di Rom
a\n2012: Dottorato in Ricerca Operativa\, Sapienza Università di Roma\n201
2-2013: Assegno di ricerca presso IASI (CNR)\, Roma\nSettembre 2013 - Febb
raio 2016: Post-Doc - Fakultät für Mathematik\,Technische Universität Dort
mund\, Germany\nMarzo 2016 – Settembre 2016: Post-doc - Institut für Mathe
matik\,Alpen-Adria-Universität Klagenfurt\, Austria\nSettembre 2016 - Marz
o 2017: Post-doc - Dipartimento di Matematica\, Università di Padova\, Ita
ly\nAprile 2017 - Marzo 2020: RTDb (SSD MAT/09)\, DIAG\, Sapienza Universi
tà di Roma\nMaggio 2019: Abilitazione Scientifica Nazionale a ricoprire il
ruolo di professore di II fascia (SSD MAT/09)\nAprile 2020 -: Professore
Associato (SSD MAT/09)\, DIAG\, Sapienza Università di Roma\n\n\n*/\n\n\nk
eywords: \n\nGlobal OptimizationMixed Integer Nonlinear ProgrammingSemideﬁ
nite Programming\n\nqualifica_rr: \n\nAssociate professors
URL;TYPE=URI:https://diag.uniroma1.it/node/12417
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