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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='font-size:14.0pt;line-height:110%;color:red'>INDUSTRIAL ENGINEERING SEMINAR<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='color:red'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='font-size:14.0pt;line-height:110%;color:red'>Date: April 25, 2014<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='font-size:14.0pt;line-height:110%;color:red'>Time: 10am-11am<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='font-size:14.0pt;line-height:110%;color:red'>Place: <a name="_GoBack"></a>102 D<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='color:red'><o:p> </o:p></span></b></p><p class=MsoPlainText align=center style='text-align:center'><b><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'>The Direct Extension of ADMM for Multi-block Convex Minimization Problems <o:p></o:p></span></b></p><p class=MsoPlainText align=center style='text-align:center'><b><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'>is Not Necessarily Convergent<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:14.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></b></p><h3 align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-add-space:auto;text-align:center'><span style='font-size:12.0pt;font-family:"Times New Roman","serif";font-weight:normal'>Yinyu Ye<o:p></o:p></span></h3><h3 align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-add-space:auto;text-align:center'><span style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black;font-weight:normal'>Professor of Management Science and Engineering<o:p></o:p></span></h3><h3 align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-add-space:auto;text-align:center'><span style='font-size:12.0pt;font-family:"Times New Roman","serif";font-weight:normal'>Director, Industrial Affiliates Program of the MS&E<o:p></o:p></span></h3><h3 align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-add-space:auto;text-align:center'><span style='font-size:12.0pt;font-family:"Times New Roman","serif";font-weight:normal'>Stanford University<o:p></o:p></span></h3><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='color:red'>Abstract</span></b><b><span style='font-size:12.0pt;line-height:110%;font-family:"Times New Roman","serif";color:red'><o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;line-height:110%'><b><span style='color:red'><o:p> </o:p></span></b></p><p class=MsoPlainText><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'>The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time — neither affirmatively proved convergence nor counter example showing its failure of convergence is known in the literature. In this paper we answer this long-standing open question: the direct extension of ADMM is not necessarily convergent. We present examples showing its failure of convergence.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'> <o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt;font-family:"Times New Roman","serif";color:red'>Biography<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></b></p><p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'>Yinyu Ye received the B.S. degree in System Engineering from the Huazhong University of Science and Technology, Wuhan, China, and the M.S. and Ph.D. degrees in Management Science & Engineering from Stanford University, Stanford. Currently, he is a full Professor of Management Science and Engineering and Institute of Computational and Mathematical Engineering and the Director of the MS&E Industrial Affiliates Program, Stanford University. His current research interests include Continuous and Discrete Optimization, Mathematical Programming, Algorithm Design and Analysis, Computational Game/Market Equilibrium, Metric Distance Geometry, Graph Realization, Dynamic Resource Allocation, and Stochastic and Robust Decision Making, etc.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";color:#1F497D'><o:p> </o:p></span></p></div></body></html>