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May  2020, 16(3): 1261-1272. doi: 10.3934/jimo.2019001

## Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities

 1 School of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan, Chongqing, 402160, China 2 College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

* Corresponding author: Minghua Li

Received  November 2016 Revised  November 2018 Published  March 2019

Fund Project: The work was supported in part by the National Natural Science Foundation of China (Grant numbers: 11301418, 11301567, 11571055), the Natural Science Foundation of Chongqing Municipal Science and Technology Commission (Grant numbers: cstc2016jcyjA0141, cstc2016jcyjA0270, cstc2018jcyjAX0226), the Basic Science and Frontier Technology Research of Yongchuan (Grant number: Ycstc, 2018nb1401), the Fundamental Research Funds for the Central Universities (Grant Number: 106112017CDJZRPY0020), the Foundation for High-level Talents of Chongqing University of Art and Sciences (Grant numbers: R2016SC13, P2017SC01), the Chongqing Key Laboratory of Group and Graph Theories and Applications and the Key Laboratory of Complex Data Analysis and Artificial Intelligence of Chongqing Municipal Science and Technology Commission

In this paper, the Clarke generalized Jacobian of the generalized regularized gap function for a nonmonotone Ky Fan inequality is studied. Then, based on the Clarke generalized Jacobian, we derive a global error bound for the nonmonotone Ky Fan inequalities. Finally, an application is given to provide a descent method.

Citation: Minghua Li, Chunrong Chen, Shengjie Li. Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1261-1272. doi: 10.3934/jimo.2019001
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##### References:
 [1] Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 [2] Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024 [3] Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709 [4] Ralf Hielscher, Michael Quellmalz. Reconstructing a function on the sphere from its means along vertical slices. Inverse Problems & Imaging, 2016, 10 (3) : 711-739. doi: 10.3934/ipi.2016018 [5] Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 [6] Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247 [7] Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 [8] Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 [9] Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 [10] Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 [11] Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 [12] Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263 [13] Min Li. A three term Polak-Ribière-Polyak conjugate gradient method close to the memoryless BFGS quasi-Newton method. Journal of Industrial & Management Optimization, 2020, 16 (1) : 245-260. doi: 10.3934/jimo.2018149 [14] Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 [15] Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069 [16] Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056

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