[Mat10] Holnapi szeminárium

[Zsófia Tardos]

Kedves Érdeklődők!

Ezúton szeretném emlékeztetni Önöket, hogy a holnapi szeminárium a
megszokottól eltérően 10:15-kor kezdődik.

Üdvözlettel,

Tardos ZsĂłfia


2014-05-18 21:43 GMT+02:00 ZsĂłfia Tardos <tardoszs at gmail.com>:

> Kedves Érdeklődők!
>
> Szeretnénk meghívni Önöket a BME Optimalizálási Szemináriumára, ahol Immanuel
> M. Bomze tart előadást "*Copositive relaxation beats Lagrangian dual
> bounds in quadratically and linearly constrained QPs" *cĂ­mmel mĂĄjus 22-ĂŠn
> csĂźtĂśrtĂśkĂśn a H306-os teremben 10:15-Ăśs kezdettel.
>
> Minden érdeklődőt szeretettel várunk!
>
> *Copositive relaxation beats Lagrangian dual bounds in quadratically and
> linearly constrained QPs*
>
> *Immanuel M. Bomze, ISOR, University of Vienna*
>
> For all-quadratic problems (without any linear constraints), it is well
> known that the semidefinite relaxation coincides basically with the
> Lagrangian dual problem. Here we study a more general case where the
> constraints can be either quadratic or linear. To be more precise, we
> include explicit sign constraints on the problem variables, and study both
> the full Lagrangian dual as well as the Semi-Lagrangian relaxation. We show
> that the stronger Semi-Lagrangian dual bounds coincide with the ones
> resulting from copositive relaxation. This way, we arrive at a full
> hierarchy of tractable conic bounds stronger than the usual Lagrangian dual
> (and thus than the SDP) bounds. We also specify sufficient conditions for
> tightness of the Semi-Lagrangian (i.e.
> copositive) relaxation and show that copositivity of the slack matrix
> guarantees global optimality for KKT points of this problem.
>
> A symmetric matrix is called copositive, if it generates a quadratic form
> taking no negative values over the positive orthant. Contrasting to
> positive-semidefiniteness, checking copositivity is NP-hard. In a
> copositive optimization problem, we have to minimize a linear function of a
> symmetric matrix over the copositive cone subject to linear constraints.
> This convex program has no non-global local solutions. On the other hand,
> there are several hard non-convex programs which can be formulated as
> copositive programs. This optimization technique shifts complexity from
> global optimization towards sheer feasibility questions. Approximation
> hierarchies offer a way to obtain approximate solutions by tractable conic
> (e.g., semidefinite) optimization techniques.
>
> A szemináriumról további információkat illetve az elhangzott előadások diáit itt találhatják:
>
>
> http://www.math.bme.hu/~diffe/szeminarium/opt.shtml#m
>
>
>
> További információ vagy hírlevélre való feliratkozás kérése esetén írjanak a következő címre: *tardoszs at gmail.com <tardoszs at gmail.com>*
>
>
> Üdvözlettel,
>
>
> Tardos ZsĂłfia
>
>
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