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SUMMARY:Jacek Gondzio: An efficient primal-dual interior point method for
large-scale truss layout optimization problems
DTSTART;VALUE=DATE-TIME:20190410T133000Z
DTEND;VALUE=DATE-TIME:20190410T143000Z
DTSTAMP;VALUE=DATE-TIME:20230602T194158Z
UID:indico-event-29@cern.ch
DESCRIPTION:il Prof. Jacek Gondzio\, \nSchool of Mathematics\, University
of Edinburgh terra' un seminario dal\ntitolo\n\nAn efficient primal-dual
interior point method for large-scale truss layout\noptimization problems\
n\nAbstract:\n\nTruss layout optimization problems are often formulated by
using a ground\nstructure approach where a set of nodes is distributed in
the design domain\nand all the possible interconnecting bars are generate
d. The main goal is\nthen to determine the optimal cross-sectional areas o
f these bars and obtain\nthe minimum weight structure that is able to sust
ain a given set of applied\nloads.\nHowever\, such consideration of the fu
ll connectivity of the nodes results in\na large number of bars making the
optimization problems computationally\nchallenging for solution technique
s. We solve the problems using a\nprimal-dual interior point method where
we employ several novel techniques\nto deal with the large size of the pro
blems.\n\nThe first step is to use a column generation procedure where the
optimal\nsolution of the large original problem is obtained by solving a
sequence of\nsmaller restricted master problems.\nHowever\, after performi
ng a few column generation iterations\, the size of\nthe restricted master
problems grows and the problems still challenge\nstandard interior point
solvers.\nTherefore\, we additionally exploit the algebraic structure of t
he problems\nand reduce the normal equations originating from the interior
point\nalgorithm to much smaller linear equation systems. We apply the\np
reconditioned conjugate gradient method to solve these reduced linear\nsys
tems. A special purpose preconditioner based on the mathematical\nproperti
es of the problem is designed. The efficiency and robustness of the\nmetho
d is supported with several numerical experiments.\n\nThis is a joint work
with Alemseged Weldeyesus.\n\nReferences:\n\nA.G. Weldeyesus and J. Gondz
io\,\nA specialized primal-dual interior point method for the plastic trus
s layout\noptimization\, Computational Optimization and Applications (2018
) 71:613--640\nhttps://doi.org/10.1007/s10589-018-0028-9\n\nA. G. Weldeyes
us\, J. Gondzio\, L. He\, M. Gilbert\, P. Shepherd and A. Tyas\,\nUsing me
mber adding technique to solve truss layout optimization problems\nwith co
nstraints on global stability\, Structural Modelling and Optimization\n(su
bmitted).\nhttp://www.maths.ed.ac.uk/~gondzio/reports/loptGlobStab.html\n\
nJ. Gondzio and P. Gonzalez-Brevis\,\nA new warmstarting strategy for the
primal-dual column generation method\nMathematical Programming\, Ser. A (2
015) 152:113--146 DOI\n10.1007/s10107-014-0779-8\n\nhttps://indico.unina.i
t/event/29/
LOCATION:Sala riunioni II livello del Dipartimento di Matematica e Applica
zioni "Renato Caccioppoli"
URL:https://indico.unina.it/event/29/
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