期刊
JOURNAL OF GLOBAL OPTIMIZATION
卷 68, 期 3, 页码 501-535出版社
SPRINGER
DOI: 10.1007/s10898-016-0488-3
关键词
Nonsmooth optimization; Nonconvex optimization; Proximal bundle methods; DC functions; Cutting plane model
资金
- Jenny and Antti Wihuri Foundation
- Turku University Foundation
- University of Turku
- Academy of Finland [289500]
- Australian Research Council [DP140103213]
- Academy of Finland (AKA) [289500, 289500] Funding Source: Academy of Finland (AKA)
In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to utilize subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain a new nonconvex cutting plane model of the original objective function, which takes into account explicitly both the convex and the concave behavior of the objective function. We design the proximal bundle method for DC programming based on this new approach and prove the convergence of the method to an -critical point. The algorithm is tested using some academic test problems and the preliminary numerical results have shown the good performance of the new bundle method. An interesting fact is that the new algorithm finds nearly always the global solution in our test problems.
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