Abstract
The logarithmic quadratic proximal (LQP) regularization is a popular and powerful proximal regularization technique for solving monotone variational inequalities with nonnegative constraints. In this paper, we propose an implementable two-step method for solving structured variational inequality problems by combining LQP regularization and projection method. The proposed algorithm consists of two parts. The first step generates a pair of predictors via inexactly solving a system of nonlinear equations. Then, the second step updates the iterate via a simple correction step. We establish the global convergence of the new method under mild assumptions. To improve the numerical performance of our new method, we further present a self-adaptive version and implement it to solve a traffic equilibrium problem. The numerical results further demonstrate the efficiency of the proposed method.
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The first author is partially supported by the National Natural Science Foundation of China (Nos. 11571087 and 71471051) and the National Natural Science Foundation of Zhejiang Province (No. LY17A010028). The third author is supported by the National Natural Science Foundation of China (Nos. 11431002 and 11401315) and Jiangsu Provincial National Natural Science Foundation of China (No. BK20140914).
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He, HJ., Wang, K., Cai, XJ. et al. An LQP-Based Two-Step Method for Structured Variational Inequalities. J. Oper. Res. Soc. China 5, 301–317 (2017). https://doi.org/10.1007/s40305-016-0147-x
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DOI: https://doi.org/10.1007/s40305-016-0147-x
Keywords
- Logarithmic quadratic proximal
- Projection method
- Variational inequality problem
- Traffic equilibrium problem