一类特殊优化问题的光滑梯度法

doi:10.15960/j.cnki.issn.1007-6093.2017.02.013

Abstract

CHEN Yuanyuan, GAO Yan, LIU Zhimin, DU Shouqiang. The smoothing gradient method for a kind of special optimization problem[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.013.

References

[1] Xiao Y H, Wang Q Y, Hu Q J. Non-smooth equations based method for l_1-norm problems with applications to compressed sensing [J]. Nonlinear Analysis, 2011, 74(11): 3570-3577.

[2] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems [J]. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597.

[3] Bruckstein A M, Donoho D L, Elad M. From sparse solutions of systems of equations to sparse modeling of signals and images [J]. SIAM Review, 2009, 51(1): 34-81.

[4] Alliney S, Ruzinsky S A. An algorithm for the minimization of mixed and norms with application to Bayesian estimation [J]. IEEE Transactions on Signal Processing, 1994, 42(3): 618-627.

[5] Liu Y W, Hu J F. A neural network for l_1-l_2 minimization based on scaled gradient projection: Application to compressed sensing [J]. Neurocomputing, 2016, 173: 988-993.

[6] Donoho D L. Compressed Sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

[7] Lustig M, Donoho D, Pauly J M. Sparse MRI: The application of compressed sensing for rapid MR imaging [J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195.

[8] Mangasarian O, Meyer R. Absolute value equations [J]. Linear Algebra and its Applications, 2006, 419(2-3): 359-367.

[9] Mangasarian O. Absolute value equation solution via concave minimization [J]. Optimization Letters, 2007, 1(1): 3-8.

[10] Iqbal J, Iqbal A, Arif M. Levenberg-Marquardt method for solving systems of absolute value equations [J]. Journal of Computational Applied Mathematics, 2015, 282: 134-138.

[11] Nocedal, Wright S J. Numerical Optimization [M]. New York: Springer, 2006.

[12] Chen X. Smoothing methods for nonsmooth, nonconvex minimization [J]. Mathematical Programming, 2012, 134: 71-99.

[1]	LI Jianling, ZHANG Hui, YANG Zhenping, JIAN Jinbao. A globally convergent SSDP algorithm without a penalty function or a filter for nonlinear semidefinite programming [J]. Operations Research Transactions, 2018, 22(4): 1-16.
[2]	. A sufficient descent conjugate gradient method for nonlinear unconstrained optimization problems [J]. Operations Research Transactions, 2018, 22(3): 59-68.
[3]	SHAO Shuting, DU Shouqiang. Smoothing cautious DPRP conjugate gradient method for solving a kind of special nonsmooth equations with max-type function [J]. Operations Research Transactions, 2018, 22(3): 69-78.
[4]	CHEN Zhongwen, ZHAO Qi, BIAN Kai. A successive linearization method with flexible penalty for nonlinear semidefinite programming [J]. Operations Research Transactions, 2017, 21(2): 84-100.
[5]	TIAN Zhaowei, ZHANG Liwei. A look at the convergence of the augmented Lagrange method for nondifferentiable convex programming from the view of a gradient method with constant stepsize [J]. Operations Research Transactions, 2017, 21(1): 111-117.
[6]	HANG Dan, YAN Shijian. Convergence of nonmonotonic Perry-Shanno's memoryless quasi-Newton method with parameters [J]. Operations Research Transactions, 2016, 20(4): 85-92.
[7]	ZHANG Qingye, GAO Yan. A hybrid bundle method for nonsmooth convex optimization [J]. Operations Research Transactions, 2016, 20(2): 113-120.
[8]	MA Guodong, JIAN Jinbao. A feasible sequential systems of linear equations algorithm for inequality constrained optimization [J]. Operations Research Transactions, 2015, 19(4): 48-58.
[9]	WAN Rui, XU Zi. On the linear convergence of the general alternating proximal gradient method for convex minimization [J]. Operations Research Transactions, 2014, 18(3): 1-12.
[10]	DU Shouqiang. Global convergence of the Levenberg-Marquardt method with Goldstein line search [J]. Operations Research Transactions, 2012, 16(4): 105-111.
[11]	ZHAO Kequan, YANG Xinmin. Characterizations of the solution set for a class of nonsmooth optimization problems [J]. Operations Research Transactions, 2012, 16(3): 109-118.
[12]	ZHAO Qi, ZHANG Yan. A Nonmonotoe Filter Method For Minimax Problems [J]. Operations Research Transactions, 2012, 16(2): 91-104.
[13]	ZHANG Yu-Nong, LI Xue-Zhong, ZHANG Zhi-Jun, LI Jun. An LVI-based Numerical Algorithm for Solving Quadratic Programming Problems [J]. Operations Research Transactions, 2012, 16(1): 21-30.
[14]	WANG Hua. A Nonmonotone Feasible SQP Method for Nonlinear Complementarity Problem [J]. Operations Research Transactions, 2011, 15(2): 85-94.

The smoothing gradient method for a kind of special optimization problem

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Recommended Articles

Metrics

Comments