<div dir="ltr">Kedves ĂrdeklĹdĹk!<div><br></div><div>EzĂşton szeretnĂŠm emlĂŠkeztetni ĂnĂśket, hogy a holnapi szeminĂĄrium a megszokottĂłl eltĂŠrĹen 10:15-kor kezdĹdik.</div><div><br></div><div>ĂdvĂśzlettel,</div><div><br></div><div>
Tardos ZsĂłfia<br><div class="gmail_extra"><br><br><div class="gmail_quote">2014-05-18 21:43 GMT+02:00 ZsĂłfia 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 ĂrdeklĹdĹk!</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">SzeretnĂŠnk <span style="background-color:rgb(255,255,204)">megh</span>Ăvni ĂnĂśket a BME <span style="background-color:rgb(255,255,204)"><span><span>OptimalizĂĄlĂĄsi</span></span></span> S<span style="background-color:rgb(255,255,204)">zeminĂĄ<span>rium</span></span><span>ĂĄra</span>, ahol </font><font style="font-family:arial,sans-serif;font-size:13.3333px" face="arial, helvetica, sans-serif">Immanuel M. Bomze tart elĹadĂĄst "</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">cĂmmel mĂĄjus 22-ĂŠn csĂźtĂśrtĂśkĂśn a H306-os teremben 10:15-Ăśs 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 ĂŠrdeklĹdĹt szeretettel vĂĄrunk!</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">
<div>
<span style="text-align:justify"><font face="arial, helvetica, sans-serif">A szeminĂĄriumrĂłl tovĂĄbbi informĂĄciĂłkat illetve az elhangzott elĹadĂĄsok diĂĄit itt talĂĄlhatjĂĄk:</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>
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</div><div style="font-family:arial,sans-serif;white-space:normal"><br></div><div style="font-family:arial,sans-serif;white-space:normal">ĂdvĂśzlettel,</div><div style="font-family:arial,sans-serif;white-space:normal"><br>
</div><div style="font-family:arial,sans-serif;white-space:normal">Tardos ZsĂłfia</div></pre></div></font></div></div>
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