Proximal Gradient-Type Algorithms for a Class of Bilevel Programming Problems

Dan Li, Shuang Chen () and Li-Ping Pang ()
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Dan Li: Information and Engineering College, Dalian University, Dalian 116622, P. R. China
Shuang Chen: Information and Engineering College, Dalian University, Dalian 116622, P. R. China
Li-Ping Pang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 05, 1-17

Abstract: A class of proximal gradient-type algorithm for bilevel nonlinear nondifferentiable programming problems with smooth substructure is developed in this paper. The original problem is approximately reformulated by explicit slow control technique to a parameterized family function which makes full use of the information of smoothness. At each iteration, we only need to calculate one proximal point analytically or with low computational cost. We prove that the accumulation iterations generated by the algorithms are solutions of the original problem. Moreover, some results of complexity of the algorithms are presented in convergence analysis. Numerical experiments are implemented to verify the efficiency of the proximal gradient algorithms for solving this kind of bilevel programming problems.

Keywords: Proximal point; nonsmooth optimization; bilevel programming (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0217595921500391

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