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[00997] A Normal Map-Based Perspective on Second Order Theory for Composite Problems: Second Order Conditions, Metric Regularity, and Nonsingularity

  • Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
  • Type : Contributed Talk
  • Abstract : Strong metric subregularity and strong metric regularity of the natural residual and the normal map are of particular importance in the convergence analysis of first-order and second-order algorithms for composite-type optimization problems. In this talk, we characterize the strong metric subregularity of the natural residual and the normal map for a general class of nonsmooth nonconvex composite functions and establish the equivalence between these conditions, the strong metric subregularity of the subdifferential, and the quadratic growth condition. Furthermore, if the nonsmooth part of the objective function has a strictly decomposable structure, then strong metric regularity of the subdifferential is shown to be equivalent to strong metric regularity of natural residual and the normal map and to a counterpart of the so-called strong second-order sufficient conditions. Finally, we provide a link of these conditions to nonsingularity of the generalized Jacobians of the normal map and natural residual.
  • Classification : 47Nxx, 47Nxx, 47Nxx, 47Nxx, 47Nxx, Variational Analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wenqing Ouyang (The Chinese University of HongKong(Shenzhen))
    • Andre Manfred Milzarek (The Chinese University of Hong Kong, Shenzhen)