[OBOE] Fwd: Is it OK to use OBOE only for a smooth function? If so, how good is the performance?

[Jean-Philippe Vial]

Hi!

Nidhi gave you the right answer. I would only qualify her assertion that
the power of OBOE is for the non-smooth case.

Exploiting the smoothness property in optimization algorithms may turn out
to be very difficult. OBOE applies to oracles delivering first order
information under the form of gradients or subgradients of a convex
objective and separating hyperplanes for the constraint domain. You can
expect that OBOE will solve such problems with reasonable efficiency,
provided the number of variables is not too large. (It does not mean that
OBOE cannot solve problems with huge number of variables using Lagrangian
duality, which reformulates the problem into one with much fewer
variables.)

Problems with smooth convex objective and  smooth convex functions for the
constraints may turn out to be very difficult for other optimization
algorithms. OBOE may be an alternative.

Regards, (and thanks to Nidhi)

Jean-Philippe Vial

2012/9/25 Tianyang Li 李天阳 Tommy Li <tmy1018 at gmail.com>

> ---------- Forwarded message ----------
> From: Nidhi Sawhney <nsawhney at gmail.com>
> Date: Tue, Sep 25, 2012 at 2:19 AM
> Subject: Re: [OBOE] Is it OK to use OBOE only for a smooth function?
> If so, how good is the performance?
> To: Tianyang Li 李天阳 Tommy Li <tmy1018 at gmail.com>
>
>
> Hello,
>
> It should be okay to use OBOE for only smooth functions, since the
> non-smooth is  a generalization of a smooth function you can either
> have the oracle return the gradient or use the setB functions. Its
> hard to say how it compares with other methods, however it is true
> that the power of OBOE is for the non-smooth case.
>
> -Nidhi
>
> On Fri, Sep 21, 2012 at 3:57 PM, Tianyang Li 李天阳 Tommy Li
> <tmy1018 at gmail.com> wrote:
> >
> > Hi,
> >
> > I'm wondering whether I can use `Oracle` like this
> >
> >     Oracle oracle(NULL, &smooth_func);
> >
> > And if so, how good is the performance compared to some other methods
> > such as interior-point methods?
> >
> > Thanks!
> >
> > Best,
> > Tianyang
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