Abstract
For nonlinear nonsmooth DC programming (difference of convex functions), we introduce a new redistributed proximal bundle method. The subgradient information of both the DC components is gathered from some neighbourhood of the current stability center and it is used to build separately an approximation for each component in the DC representation. Especially we employ the nonlinear redistributed technique to model the second component of DC function by constructing a local convexification cutting plane. The corresponding convexification parameter is adjusted dynamically and is taken sufficiently large to make the `augmented' linearization errors nonnegative. Based on above techniques we obtain a new convex cutting plane model of the original objective function. Based on this new approximation the redistributed proximal bundle method is designed and the convergence of the proposed algorithm to a Clarke stationary point is proved. A simple numerical experiment is given to show the validity of the presented algorithm.
Funding: The first author was supported by the National Nature Science Foundation of China (61877032). The third author was supported by the National Nature Science Foundation of China (11601061) and the Fundamental Research Funds for the Central Universities of China (DUT16LK07). The fourth author was supported by the Science Foundation of Educational Committee of Liaoning Province (LQ2019019).
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