A filter proximal bundle method for nonsmooth nonconvex constrained optimization

Najmeh Hoseini Monjezi () and S. Nobakhtian ()
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Najmeh Hoseini Monjezi: Faculty of Mathematics and Statistics, University of Isfahan
S. Nobakhtian: Faculty of Mathematics and Statistics, University of Isfahan

Journal of Global Optimization, 2021, vol. 79, issue 1, No 1, 37 pages

Abstract: Abstract 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 the constraint. 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.

Keywords: Nonsmooth optimization; Nonconvex optimization; Proximal bundle method; Filter technique; Global convergence; 90C26; 65K05; 49J52 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00939-3

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