Monday, June 15, 2015 4:15 pm
-
4:15 pm
EDT (GMT -04:00)
Title: The generalized Trust region subproblem (GTRS)
| Speaker: | Dessalegn Hirpa |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract: The trust region subproblem (TRS)-the minimization of quadratic objective subject to one quadratic constraint- has many applications in diverse areas. In particular, it determines the step in trust region algorithm.
The
GTRS
generalizes
the
TRS
in
a
sense
that
it
consists
in
minimizing
a general quadratic objective subject to an upper and lower bounded
general quadratic constraint. This means, there is no definiteness
assumption on either quadratic functions. The paper characterizes the
optimality conditions for this implicit convex problem under a constraint qualification and show that it can be assumed without loss of generality. The problem is classified in to an easy and hard instances, and the paper demonstrates that the upper and lower bounded general problem can be reduced to an equivalent equality constrained problem and possibly solving the sparse system.
The paper also discusses how the Rendl-Wolkowicz algorithm proposed in
Fortin and Wolkowicz and Rendl and Wolkowicz can be extended to solve
the resulting equality constrained problem, highlighting the connection between the GTRS and the problem of finding minimum generalized eigenvalues of a parameterized matrix pencil. Finally, a numerical result is presented to illustrate the algorithm.
a general quadratic objective subject to an upper and lower bounded
general quadratic constraint. This means, there is no definiteness
assumption on either quadratic functions. The paper characterizes the
optimality conditions for this implicit convex problem under a constraint qualification and show that it can be assumed without loss of generality. The problem is classified in to an easy and hard instances, and the paper demonstrates that the upper and lower bounded general problem can be reduced to an equivalent equality constrained problem and possibly solving the sparse system.
The paper also discusses how the Rendl-Wolkowicz algorithm proposed in
Fortin and Wolkowicz and Rendl and Wolkowicz can be extended to solve
the resulting equality constrained problem, highlighting the connection between the GTRS and the problem of finding minimum generalized eigenvalues of a parameterized matrix pencil. Finally, a numerical result is presented to illustrate the algorithm.
The
presentation
will
be
based
on
the
following
manuscript:
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more
information
about
our
reading
group,
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visit
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