Abstract
A proximal bundle method is presented for minimizing a nonsmooth convex functionf. At each iteration, it requires only one approximate evaluation off and its ε-subgradient, and it finds a search direction via quadratic programming. When applied to the Lagrangian decomposition of convex programs, it allows for inexact solutions of decomposed subproblems; yet, increasing their required accuracy automatically, it asymptotically finds both the primal and dual solutions. It is an implementable approximate version of the proximal point algorithm. Some encouraging numerical experience is reported.
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Communicated by O. L. Mangasarian
The author thanks two anonymous referees for their valuable comments.
Research supported by the State Committee for Scientific Research under Grant 8550502206.
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Kiwiel, K.C. Approximations in proximal bundle methods and decomposition of convex programs. J Optim Theory Appl 84, 529–548 (1995). https://doi.org/10.1007/BF02191984
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DOI: https://doi.org/10.1007/BF02191984