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CATEGORIES:CUED Control Group Seminars
SUMMARY:Matrix Inequalities with Matrix Unknowns - Profess
or Bill Helton (Mathematics Department\, UC San Di
ego)
DTSTART;TZID=Europe/London:20100416T140000
DTEND;TZID=Europe/London:20100416T150000
UID:TALK24218AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24218
DESCRIPTION:Linear matrix inequalities LMIs are common in many
areas: control systems\, combinatorial optimizati
on\, statistics\, etc. They often have unknowns\n
x= ( x_1\, ... \,x_n) with x_j scalars\, but in ma
ny problems of control\, certainly the classical o
nes\, the unknowns enter naturally as matrices.\n\
nThe talk treats several topics involving LMIs wit
h matrix unknowns:\n\nA basic question in light of
the fact that convexity\, a seemingly much weaker
condition than being an LMI\, guarantees numerica
l success is: \n_How much more restricted are LMIs
than Convex MIs?_ \nIt turns out that scalar unk
nowns vs matrix unknowns makes a huge difference i
n the answer.\n\nCan we transform a problem to bei
ng convex?\n\nLMI domination: L dominates \\L mea
ns L(x) is positive definite implies \\L(x) is pos
itive definite. Checking for domination numericall
y can be NP hard. However\, we relax the problem b
y insisting on domination whenever the unknowns x_
j are matrices.\nThere is an elegant algebraic cha
racterization of relaxed LMI domination and numeri
cal solution is no longer NP hard. Roughly what we
observed is that this matrix relaxation correspon
ds exactly to a very natural procedure in modern
in modern functional analysis.\n
LOCATION: Cambridge University Engineering Department\, LR6
CONTACT:Dr Ioannis Lestas
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