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SUMMARY:Convex relaxations in combinatorial optimization and robust contro
l - Prof George Halikias (City University\, London)
DTSTART;VALUE=DATE-TIME:20180509T140000
DTEND;VALUE=DATE-TIME:20180509T150000
UID:https://talks.ox.ac.uk/talks/id/5bd7d06a-a9f8-492c-8492-4f99944cefaf/
DESCRIPTION:Convex relaxation methods are presented for solving two distin
ct (and apparently unconnected) computationally intractable (NP-hard) prob
lems. \n\nThe first is the classical combinatorial Quadratic Integer Progr
amming (QIP) problem\, which has numerous applications in Control\, OR\, S
tatistics and graph theory. The proposed technique explores the properties
of the optimal solution of the dual problem in order to reduce the dualit
y gap. This is achieved by solving a problem of the same form as the prima
l but of reduced rank\, involving the enumeration of the vertices of a zon
otope in a low-dimensional space which can be performed via a polynomial-t
ime algorithm. \n\nThe second problem is the calculation of the "structure
d singular value" (mu) of a matrix\, which is still the main computational
bottleneck in robust control. Our approach proceeds by formulating and so
lving a sequence of "relaxed" structured distance-to-singularity problems.
Bounds on the structured singular value are obtained by specializing the
results to uncertainty structures involving simultaneous spectral-radius a
nd norm constraints. Provided the solution (or a "good" bound) of a reduce
d-rank mu-problem can be obtained\, our method produces an upper bound bou
nd for the original problem which breaches the convex relaxation ("D-itera
tion") bound\, via the solution of an eigenvalue problem. \n\nThe similari
ties between the techniques corresponding to each problem (QIP and mu) are
highlighted\, which suggests that the could be instances of a single gene
ral methodology in the area of convex relaxations. \nSpeakers:\nProf Georg
e Halikias (City University\, London)
LOCATION:Venue to be announced
URL:https://talks.ox.ac.uk/talks/id/5bd7d06a-a9f8-492c-8492-4f99944cefaf/
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DESCRIPTION:Talk:Convex relaxations in combinatorial optimization and robu
st control - Prof George Halikias (City University\, London)
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