<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-size:small"><div><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">  Monday, December 2nd at 11:00 am</font></font><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Where:</b>     </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">TTIC, 6045 S. Kenwood Avenue, 5th Floor, Room 526</font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b>       </font></font></font>Lorenzo Orecchia, University of Chicago</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">    </font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">  </font></font></font></p></div><div><div><font face="arial, sans-serif"><b>Title:        </b></font><span style="color:rgb(0,0,0)">First-Order Optimization and the Calculus of Variations</span></div><div><br></div><div><font face="arial, sans-serif"><b>Abstract: </b></font><span style="color:black">We present a novel approach to analyze and design first-order methods for convex optimization via the calculus of variations. Specifically, we show that the continuous-time dynamics underlying these methods arise as the unique solutions of the minimization of natural convex functionals over the space of absolutely continuous paths from a given starting point. While previous work has characterized these continuous-time dynamics as critical points of certain functionals, i.e., solutions to Euler-Lagrange equations, our work is the first to give a convex formulation of these functionals. An interesting upshot of this work is that the problem of designing continuous-time first-order methods for convex optimization is itself a convex optimization problem.</span></div><p class="MsoNormal"><span style="color:black">No previous knowledge of the calculus of variations is necessary, as I will introduce its basics from a TCS viewpoint within the talk.</span></p></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><div><b style="font-family:arial,sans-serif">Host:</b><span style="font-family:arial,sans-serif"> <a href="mailto:madhurt@ttic.edu" target="_blank">Madhur Tulsiani</a></span><a href="mailto:madhurt@ttic.edu" target="_blank"><br></a></div><div><br></div><div><br></div><div><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif">For more information on the </span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif">colloquium</span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif"> series or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" target="_blank" style="font-size:12.8px;font-family:arial,helvetica,sans-serif">http://www.ttic.edu/colloquium.php</a>  <br></div><div><br></div></div></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 517</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div></div></div></div></div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Dec 1, 2019 at 5:57 PM Mary Marre <<a href="mailto:mmarre@ttic.edu">mmarre@ttic.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr"><div style="font-size:small"><div><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">  Monday, December 2nd at 11:00 am</font></font><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Where:</b>     </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">TTIC, 6045 S. Kenwood Avenue, 5th Floor, Room 526</font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b>       </font></font></font>Lorenzo Orecchia, University of Chicago</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">    </font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">  </font></font></font></p></div><div><div><font face="arial, sans-serif"><b>Title:        </b></font><span style="color:rgb(0,0,0)">First-Order Optimization and the Calculus of Variations</span></div><div><br></div><div><font face="arial, sans-serif"><b>Abstract: </b></font><span style="color:black">We present a novel approach to analyze and design first-order methods for convex optimization via the calculus of variations. Specifically, we show that the continuous-time dynamics underlying these methods arise as the unique solutions of the minimization of natural convex functionals over the space of absolutely continuous paths from a given starting point. While previous work has characterized these continuous-time dynamics as critical points of certain functionals, i.e., solutions to Euler-Lagrange equations, our work is the first to give a convex formulation of these functionals. An interesting upshot of this work is that the problem of designing continuous-time first-order methods for convex optimization is itself a convex optimization problem.</span></div><p class="MsoNormal"><span style="color:black">No previous knowledge of the calculus of variations is necessary, as I will introduce its basics from a TCS viewpoint within the talk.</span></p></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><div><b style="font-family:arial,sans-serif">Host:</b><span style="font-family:arial,sans-serif"> <a href="mailto:madhurt@ttic.edu" target="_blank">Madhur Tulsiani</a></span><a href="mailto:madhurt@ttic.edu" target="_blank"><br></a></div><div><br></div><div><br></div><div><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif">For more information on the </span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif">colloquium</span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif"> series or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" style="font-size:12.8px;font-family:arial,helvetica,sans-serif" target="_blank">http://www.ttic.edu/colloquium.php</a>  <br></div><div><br></div></div><div><br></div></div><div><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 517</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div></div></div></div></div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Nov 25, 2019 at 6:07 PM Mary Marre <<a href="mailto:mmarre@ttic.edu" target="_blank">mmarre@ttic.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-size:small"><div><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">  Monday, December 2nd at 11:00 am</font></font><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Where:</b>     </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">TTIC, 6045 S. Kenwood Avenue, 5th Floor, Room 526</font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b>       </font></font></font>Lorenzo Orecchia, University of Chicago</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">    </font></font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="vertical-align:inherit"><font style="vertical-align:inherit">  </font></font></font></p></div><div><div><font face="arial, sans-serif"><b>Title:        </b></font><span style="color:rgb(0,0,0)">First-Order Optimization and the Calculus of Variations</span></div><div><br></div><div><font face="arial, sans-serif"><b>Abstract: </b></font><span style="color:black">We present a novel approach to analyze and design first-order methods for convex optimization via the calculus of variations. Specifically, we show that the continuous-time dynamics underlying these methods arise as the unique solutions of the minimization of natural convex functionals over the space of absolutely continuous paths from a given starting point. While previous work has characterized these continuous-time dynamics as critical points of certain functionals, i.e., solutions to Euler-Lagrange equations, our work is the first to give a convex formulation of these functionals. An interesting upshot of this work is that the problem of designing continuous-time first-order methods for convex optimization is itself a convex optimization problem.</span></div><p class="MsoNormal"><span style="color:black">No previous knowledge of the calculus of variations is necessary, as I will introduce its basics from a TCS viewpoint within the talk.</span></p></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><font face="arial, sans-serif"><b><br></b></font></div><div><div><b style="font-family:arial,sans-serif">Host:</b><span style="font-family:arial,sans-serif"> <a href="mailto:madhurt@ttic.edu" target="_blank">Madhur Tulsiani</a></span><a href="mailto:madhurt@ttic.edu" target="_blank"><br></a></div><div><br></div><div><br></div><div><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif">For more information on the </span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif"><span>colloquium</span></span><span style="font-size:12.8px;font-family:arial,helvetica,sans-serif"> series or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" style="font-size:12.8px;font-family:arial,helvetica,sans-serif" target="_blank">http://www.ttic.edu/<span>colloquium</span>.php</a>  <br></div><div><br></div></div><div><br></div><div><br></div><div><br></div></div><div><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><font face="arial, helvetica, sans-serif">Mary C. Marre</font><div><font face="arial, helvetica, sans-serif">Administrative Assistant</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">6045 S. Kenwood Avenue</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Room 517</font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i></div><div><i><font face="arial, helvetica, sans-serif">p:(773) 834-1757</font></i></div><div><i><font face="arial, helvetica, sans-serif">f: (773) 357-6970</font></i></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</blockquote></div></div>
</blockquote></div></div>