An approximate bundle method for solving nonsmooth equilibrium problems

Fan-Yun Meng (), Li-Ping Pang (), Jian Lv () and Jin-He Wang ()
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Fan-Yun Meng: Dalian University of Technology
Li-Ping Pang: Dalian University of Technology
Jian Lv: Dalian University of Technology
Jin-He Wang: Qingdao Technological University

Journal of Global Optimization, 2017, vol. 68, issue 3, No 3, 537-562

Abstract: Abstract We present an approximate bundle method for solving nonsmooth equilibrium problems. An inexact cutting-plane linearization of the objective function is established at each iteration, which is actually an approximation produced by an oracle that gives inaccurate values for the functions and subgradients. The errors in function and subgradient evaluations are bounded and they need not vanish in the limit. A descent criterion adapting the setting of inexact oracles is put forward to measure the current descent behavior. The sequence generated by the algorithm converges to the approximately critical points of the equilibrium problem under proper assumptions. As a special illustration, the proposed algorithm is utilized to solve generalized variational inequality problems. The numerical experiments show that the algorithm is effective in solving nonsmooth equilibrium problems.

Keywords: Equilibrium problems; Bundle methods; Approximate function and subgradient; 90C25; 49J40; 90C20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-016-0490-9

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