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Paper   IPM / M / 16542
School of Mathematics
  Title:   A filter proximal bundle method for nonsmooth nonconvex constrained optimization
  Author(s):  Soghra Nobakhtian (Joint with N. Hoseini Monjezi)
  Status:   Published
  Journal: J. Glob. Optim.
  Vol.:  79
  Year:  2021
  Pages:   1-37
  Supported by:  IPM
A filter proximal bundle algorithm is presented for nonsmooth nonconvex constrained optimization problems. The new algorithm is based on the proximal bundle method and utilizes the improvement function to regularize constraints. At every iteration by solving a convex piecewise-linear subproblem a trial point is obtained. The process of the filter technique is employed either to accept the trial point as a serious iterate or to reject it as a null iterate. Under some mild and standard assumptions, and for every possible choice of a starting point, it is shown that every accumulation point of the sequence of serious iterates is feasible. In addition, there exists at least one accumulation point which is stationary for the improvement function. Finally, some encouraging numerical results show that the proposed algorithm is effective.

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