A globally convergent proximal Newton-type method in nonsmooth convex optimization

  title={A globally convergent proximal Newton-type method in nonsmooth convex optimization},
  author={Boris S. Mordukhovich and Xiaoming Yuan and Shangzhi Zeng and Jin Zhang},
  journal={Mathematical Programming},
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of variational analysis, we establish implementable results on the global convergence of the proposed algorithm as well as its local convergence with superlinear and quadratic rates. For certain structural problems, the obtained local convergence conditions do not… 
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