<div dir="ltr">Kedves Érdeklődők!<div><br></div><div>Ezúton szeretném emlékeztetni Önöket, hogy a holnapi szeminárium a megszokottól eltérően 10:15-kor kezdődik.</div><div><br></div><div>Üdvözlettel,</div><div><br></div><div>
Tardos Zsófia<br><div class="gmail_extra"><br><br><div class="gmail_quote">2014-05-18 21:43 GMT+02:00 Zsófia Tardos <span dir="ltr"><<a href="mailto:tardoszs@gmail.com" target="_blank">tardoszs@gmail.com</a>></span>:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><span style="font-size:13px;font-family:arial,helvetica,sans-serif">Kedves Érdeklődők!</span><br style="font-family:arial,sans-serif;font-size:13px">
<div style="font-family:arial,sans-serif;font-size:13.3333px"><font face="arial, helvetica, sans-serif"><br></font></div><div><font style="font-family:arial,sans-serif;font-size:13.3333px" face="arial, helvetica, sans-serif">Szeretnénk <span style="background-color:rgb(255,255,204)">megh</span>ívni Önöket a BME <span style="background-color:rgb(255,255,204)"><span><span>Optimalizálási</span></span></span> S<span style="background-color:rgb(255,255,204)">zeminá<span>rium</span></span><span>ára</span>, ahol </font><font style="font-family:arial,sans-serif;font-size:13.3333px" face="arial, helvetica, sans-serif">Immanuel M. Bomze tart előadást "</font><span style="font-family:arial,helvetica,sans-serif;font-size:13.3333px;text-align:center"><span style="line-height:14px"><i>Copositive relaxation beats Lagrangian dual bounds in quadratically and linearly constrained QPs" </i></span></span><span style="font-family:arial,helvetica,sans-serif;font-size:13.3333px">címmel május 22-én csütörtökön a H306-os teremben 10:15-ös kezdettel. </span></div>
<div style="font-family:arial,sans-serif;font-size:13.3333px"><font face="arial, helvetica, sans-serif"><br></font></div><div style="font-family:arial,sans-serif;font-size:13.3333px"><font face="arial, helvetica, sans-serif">Minden érdeklődőt szeretettel várunk!</font></div>
<div style="font-family:arial,sans-serif;font-size:13.3333px"><font face="arial, helvetica, sans-serif"><br></font></div><div style="font-family:arial,sans-serif;font-size:13.3333px"><div style="text-align:center"><b><span style="font-family:arial,helvetica,sans-serif;font-size:13.3333px;text-align:center"><span style="line-height:14px">Copositive relaxation beats Lagrangian dual bounds in quadratically and linearly constrained QPs</span></span></b></div>
<div style="font-size:13.3333px;text-align:center"><b>
</b><span style="font-size:small;text-align:start;white-space:pre-wrap"><b><br></b></span></div><div style="text-align:center"><b>Immanuel M. Bomze, <i>ISOR, University of Vienna</i></b><br>
<br><div style="text-align:left">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.<br>
copositive) relaxation and show that copositivity of the slack matrix<br>
guarantees global optimality for KKT points of this problem.<br>
<br>
A symmetric matrix is called copositive, if it generates a quadratic
form taking no negative values over the positive orthant. Contrasting to<br>
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.</div></div></div><div><font face="arial, helvetica, sans-serif"><div><br></div><div><pre style="white-space:pre-wrap;font-size:13px"><div style="font-family:arial,sans-serif;white-space:normal">
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<span style="text-align:justify"><font face="arial, helvetica, sans-serif">A szemináriumról további információkat illetve az elhangzott előadások diáit itt találhatják:</font></span></div><div><span style="text-align:justify"><font face="arial, helvetica, sans-serif"><br>
</font></span></div><div><font face="arial, helvetica, sans-serif"><a href="http://www.math.bme.hu/%7Ediffe/szeminarium/opt.shtml#m" target="_blank">http://www.math.bme.hu/~diffe/<span style="background-color:rgb(255,255,204);color:rgb(34,34,34)">szeminarium</span>/opt.shtml#m</a><br>
<span style="text-align:justify"><br></span></font></div><div><br></div><div>További információ vagy hírlevélre való feliratkozás kérése esetén írjanak a következő címre: <span style="background-color:rgb(255,255,204)"><u><a href="mailto:tardoszs@gmail.com" target="_blank">tardoszs@gmail.com</a></u></span></div>
</div><div style="font-family:arial,sans-serif;white-space:normal"><br></div><div style="font-family:arial,sans-serif;white-space:normal">Üdvözlettel,</div><div style="font-family:arial,sans-serif;white-space:normal"><br>
</div><div style="font-family:arial,sans-serif;white-space:normal">Tardos Zsófia</div></pre></div></font></div></div>
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