An Approximate Sequential Bundle Method for Solving a Convex Nondifferentiable Bilevel Programming Problem
Jie Shen, Li-Ping Pang, Xi-Jun Liang, Zun-Quan Xia
Journal of Advances in Mathematics and Computer Science · pp. 2917–2928 · Published 1 Aug 2014
10.9734/BJMCS/2014/12022Abstract
By combining two bundle methods, PBMASL (proximal bundle method with approximate subgradient linearizations) and DPLBM (descent proximal level bundle method), we present an approximate sequential bundle algorithm for solving a bilevel programming problem with a nondifferentiable convex objective function and two separable constraints. In the proposed algorithm, the values of the objective function in the constraints and its subgradients are computed approximately, the estimates of the tolerances are not required for convergence proof. The presented results improve and extend the earlier work.
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