Foundations of Primal-Dual Symmetric Interior-Point Methods for Convex Optimization
| Speaker: | Levent Tuncel |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics 3 (M3) 2134 |
Abstract:
In
the
theory
of
modern
interior-point
algorithms,
approaches
that
treat
primal
and
the
dual
problems
in
a
symmetric
way
have
led
to
some
of
the
deepest
theoretical
results
as
well
as
some
of
the
most
successful
software
in
that
area.
I
will
present
some
mathematical
foundations
for
the
design
and
analysis
of
primal-dual
symmetric
algorithms
for
convex
optimization
problems.
These
foundations
make
the
generalization
of
such
methods
from
linear
and
semidefinite
optimization
settings
to
general
convex
optimization
setting
possible.
I
will
conclude
with
a
complexity
analysis
which
applies
to
a
wide
range
of
primal-dual
interior-point
algorithms.
Our
bound
on
the
number
of
iterations
extends
the
current
best
iteration
complexity
bounds
from
the
special
cases
of
linear
and
semidefinite
optimization
to
the
general
convex
optimization
setting.
This
talk
is
based
on
joint
work
with
Tor
Myklebust.