回到顶部

机器学习与优化方法1-AIRS in the AIR

2022年10月11日 9:00 ~ 2022年10月11日 11:30
线上活动 (支持回放)

收起

活动票种
    付费活动,请选择票种
    展开活动详情

    活动内容收起

    Title: Deterministically Constrained Stochastic Optimization


    Abstract: 

    I will present the recent work by my research group on the design, analysis, and implementation of algorithms for solving continuous nonlinear optimization problems that involve a stochastic objective function and deterministic constraints.  The talk will focus on our sequential quadratic optimization (commonly known as SQP) methods for cases when the constraints are defined by nonlinear systems of equations and inequalities.  Our methods are applicable for solving various types of problems, such as for training machine learning (e.g., deep learning) models with constraints.  Our work focuses on the "fully stochastic" regime in which only stochastic gradient estimates are employed, for which we have derived convergence-in-expectation results and worst-case iteration complexity bounds that are on par with stochastic gradient methods for the unconstrained setting.  I will also discuss the various extensions that my group is exploring.


    Bio: 

    Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University. Prior to joining Lehigh, he received his bachelor's degree from the College of William and Mary, received his master's and doctoral degrees from the Department of Industrial Engineering and Management Science at Northwestern University, and worked as a Postdoctoral Researcher in the Courant Institute of Mathematical Sciences at New York University. His research focuses on the design, analysis, and implementation of numerical methods for solving large-scale nonlinear optimization problems. He received an Early Career Award from the Advanced Scientific Computing Research program of the U.S. Department of Energy, and has had other funded projects with the U.S. National Science Foundation, Office of Naval Research, and Advanced Research Projects Agency - Energy. He received, along with Leon Bottou (Facebook AI Research) and Jorge Nocedal (Northwestern), the 2021 SIAM/MOS Lagrange Prize in Continuous Optimization. He was awarded, with James V. Burke (U. of Washington), Adrian Lewis (Cornell), and Michael Overton (NYU), the 2018 INFORMS Computing Society Prize. He and team members Daniel Molzahn (Georgia Tech), Andreas Waechter (Northwestern), Ermin Wei (Northwestern), and Elizabeth Wong (UC San Diego) were awarded second place in the ARPA-E Grid Optimization Competition in 2020. He currently serves as an Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Mathematics of Operations Research, IMA Journal of Numerical Analysis, and Mathematical Programming Computation. He previously served as the Vice Chair for Nonlinear Programming for the INFORMS Optimization Society and is currently very active in professional societies and groups related to mathematical optimization, including INFORMS, the Mathematics Optimization Society, and the SIAM Activity Group on Optimization.


    Title: Constraint Dissolving Approaches for a Class of Riemannian Optimization Problems


    Abstract :

    We propose constraint   dissolving approaches for optimization problems over  a class of Riemannian manifolds. In these   proposed approaches, solving a Riemannian optimization problem is transferred   into the unconstrained minimization of a constraint dissolving function named   CDF. Different from existing exact penalty functions, the exact gradient and   Hessian of CDF are easy to compute. We study the theoretical properties of   CDF and prove that the original problem and CDF have the same first-order and   second-order stationary points, local minimizers, and Łojasiewicz exponents in a neighborhood of the   feasible region. Remarkably, the convergence properties of our proposed   constraint dissolving approaches can be directly inherited from the existing   rich results in unconstrained optimization. Therefore, the proposed   constraint dissolving approaches build up short cuts from unconstrained   optimization to Riemannian optimization. Several illustrative examples   further demonstrate the potential of the proposed approaches.

       

    Bio:

    Dr. Xin Liu, “Feng Kang” Distinguished Professor of the Academy of Mathematics and Systems Science, Chinese Academy Sciences. He got his bachelor degree from the School of Mathematical Sciences, Peking University in 2004, and PhD from the University of Chinese Academy of Sciences in 2009. His research interests include the optimization problems over the Stiefel manifold, linear and nonlinear eigenvalue problems, nonlinear least squares and distributed optimization. Dr. Xin Liu was granted the Excellent Young Scientists Fund from NSFC in 2016, the Science and Technology Award for Youth from ORSC in 2016, the Fifth CSIAM Young Scholar Prize in 2020 and the National Science Fund of China for Distinguished Young Scholars in 2021. He serves as an associate editor of “Mathematical Programming Computation”, “Asia-Pacific Journal of Operational Research”, “Operations Research Transactions”, “Journal of Computational Mathematics” and “Journal of Industrial and Management Optimization”.




    举报活动

    活动标签

    最近参与

    • Livian
      收藏

      (2年前)

    • ZMurphy
      收藏

      (2年前)

    • Evan
      报名

      (2年前)

    • 苏苏'
      报名

      (2年前)

    • 666
      报名

      (2年前)

    • 大格传奇
      报名

      (2年前)

    您还可能感兴趣

    您有任何问题,在这里提问!

    为营造良好网络环境,评价信息将在审核通过后显示,请规范用语。

    全部讨论

    活动主办方更多

    微信扫一扫

    分享此活动到朋友圈

    免费发布