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This ORFE talk might be of interest to the theory folks.
<div>Philippe<br>
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<div>--</div>
<div>Philippe Rigollet</div>
<div><a href="http://www.princeton.edu/~rigollet">www.princeton.edu/~rigollet</a></div>
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<div>Begin forwarded message:</div>
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<span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>From:
</b></span><span style="font-family:'Helvetica'; font-size:medium;">Lisa Glass <<a href="mailto:lglass@PRINCETON.EDU">lglass@PRINCETON.EDU</a>><br>
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<span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>Subject:
</b></span><span style="font-family:'Helvetica'; font-size:medium;"><b>[ORFE seminars] ORFE Seminar: Amir Ali Ahmadi, February 12 at 4:30pm, Sherrerd Hall 101</b><br>
</span></div>
<div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;">
<span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>Date:
</b></span><span style="font-family:'Helvetica'; font-size:medium;">February 6, 2013 12:14:27 PM EST<br>
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<span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>To:
</b></span><span style="font-family:'Helvetica'; font-size:medium;"><<a href="mailto:ORFE-TALKS@Princeton.EDU">ORFE-TALKS@Princeton.EDU</a>><br>
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<span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>Reply-To:
</b></span><span style="font-family:'Helvetica'; font-size:medium;">Lisa Glass <<a href="mailto:lglass@PRINCETON.EDU">lglass@PRINCETON.EDU</a>><br>
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=== ORFE Seminar Announcement === <b><br>
<br>
</b>DATE: Tuesday, February 12, 2013 <br>
<br>
TIME: 4:30pm <br>
<br>
LOCATION: Room 101, Sherrerd Hall <br>
<br>
SPEAKER: Amir Ali Ahmadi, IBM Watson Research Center<br>
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TITLE:<b style=""> </b>The Interplay of Convexity and Algorithmic Algebra in Oprimization and Systems Analysis<br>
<br>
ABSTRACT:
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">Exciting recent developments at the interface of computational algebra and convex optimiza-<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height:
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">tion have led to major algorithmic advances in a broad range of problems in optimization<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height:
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">and systems theory. I will start this talk by giving an overview of these techniques and<o:p></o:p></span></p>
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<span style="font-size:
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">theory. I will then focus on two recent results on computational and algebraic aspects of<o:p></o:p></span></p>
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<i style="mso-bidi-font-style:
normal"><span style="font-size:12.0pt;mso-bidi-font-family:"Times
New Roman"">convexity</span></i><span style="font-size:12.0pt;mso-bidi-font-family:"Times
New Roman""> in optimization:
(i) I will show that deciding convexity of polynomials of degree as<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height:
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">low as four is strongly NP-hard. This solves a problem that appeared as one of seven open<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">problems in complexity theory for numerical optimization in 1992. (ii) I will introduce an<o:p></o:p></span></p>
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<span style="font-size:
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<i style="mso-bidi-font-style:
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New Roman"">as sum-of-squares-convexity</span></i><span style="font-size:12.0pt;mso-bidi-font-family:
"Times New Roman"">
and present a complete characterization of the cases where it<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">is equivalent to convexity. This characterization draws an interesting parallel to a seminal<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">1888 result of Hilbert in real algebraic geometry.<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">In the final part of the talk, I will move on to a problem with numerous applications in<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">engineering and sciences: understanding the asymptotic behavior of linear dynamical systems<o:p></o:p></span></p>
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<span style="font-size:
12.0pt;mso-bidi-font-family:"Times New Roman"">under uncertainty. I will tackle this problem with a novel class of SDP-based algorithms (with<o:p></o:p></span></p>
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<span style="font-size:
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