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Paper   IPM / M / 16719
School of Mathematics
  Title:   Convergence of the proximal bundle algorithm for nonsmooth nonconvex optimization problems
  Author(s):  Najmeh Hoseini Monjezi (Joint with S. Nobakhtian)
  Status:   Published
  Journal: Optim. Lett
  Year:  2021
  Pages:   DOI: 10.1007/s11590-021-01787-0
  Supported by:  IPM
A proximal bundle algorithm is proposed for solving unconstrained nonsmooth nonconvex optimization problems. At each iteration, using already generated information, the algorithm defines a convex model of the augmented objective function. Then by solving a quadratic subproblem a new candidate iterate is obtained and the algorithm is repeated. The novelty in our approach is that the objective function can be any arbitrary locally Lipschitz function without any additional assumptions. The global convergence, starting from any point, is also studied. At the end, some encouraging numerical results with a MATLAB implementation are reported.

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