Smoothing techniques in solving non-Lipschitz absolute value equations

References

• L. Abdallah, M. Haddou, and T. Migot, Solving absolute value equation using complementarity and smoothing functions, J Comput Appl Math 327 (2018), pp. 196–207.
   Web of Science ®Google Scholar
• A.M. Bagirov, A. Al Nuaimat, and N. Sultanova, Hyperbolic smoothing function method for minimax problems, Optimization 62 (6) (2013), pp. 759–782.
   Web of Science ®Google Scholar
• A. Ben-Tal and M. Teboulle, A smoothing technique for nondifferentiable optimization problems, in Optimization, Szymon Dolecki, ed., Springer Berlin Heidelberg, Berlin, Heidelberg, 1989, pp. 1–11.
   Google Scholar
• Dimitri P. Bertsekas, Nondifferentiable optimization via approximation, Springer Berlin Heidelberg, Berlin, Heidelberg, 1975. pp. 1–25.
   Google Scholar
• Louis Caccetta, Biao Qu, and Guanglu Zhou, A globally and quadratically convergent method for absolute value equations, Comput Optim Appl 48 (1) (2011), pp. 45–58.
   Web of Science ®Google Scholar
• Xiaojun Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math Program 134 (1) (2012), pp. 71–99.
   Web of Science ®Google Scholar
• Chunhui Chen and O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Comput Optim Appl 5 (2) (1996), pp. 97–138.
   Google Scholar
• Cairong Chen, Dongmei Yu, Deren Han, and Changfeng Ma, A non-monotone smoothing newton algorithm for solving the system of generalized absolute value equations, 2021.
   Google Scholar
• C. Grossman, Smoothing techniques for exact penalty function methods, American Mathematical Society, Providence, Rhode Island, 2016, pp. 249–265.
   Google Scholar
• Fakhrodin Hashemi and Saeed Ketabchi, Numerical comparisons of smoothing functions for optimal correction of an infeasible system of absolute value equations, Numer Algebra Control Optim 10 (1) (2020), pp. 13–21.
   Web of Science ®Google Scholar
• Sheng-Long Hu and Zheng-Hai Huang, A note on absolute value equations, Optim Lett 4 (3) (2010), pp. 417–424.
   Web of Science ®Google Scholar
• Xiaoqin Jiang, A smoothing Newton method for solving absolute value equations, Atlantis Press, 2013/04, pp. 483–489.
   Google Scholar
• Zhuling Jiang and Jicheng Li, Solving tensor absolute value equation, Appl Numer Math 170 (2021), pp. 255–268.
   Web of Science ®Google Scholar
• Xiaoqin Jiang and Ying Zhang, A smoothing-type algorithm for absolute value equations, J Ind Manag Optim 9 (4) (2013), pp. 789–798.
   Web of Science ®Google Scholar
• Saeed Ketabchi and Hossein Moosaei, Minimum norm solution to the absolute value equation in the convex case, J Optim Theory Appl 154 (3) (2012), pp. 1080–1087.
   Web of Science ®Google Scholar
• Ying-Ying Lian, Cui-Xia Li, and Shi-Liang Wu, Weaker convergent results of the generalized newton method for the generalized absolute value equations, J Comput Appl Math 338 (2018), pp. 221–226.
   Web of Science ®Google Scholar
• Yan-Di Liu, Jein-Shan Chen, Chun-Hsu Ko, and Sheng-Pen Wang, New smoothing functions for solving a system of equalities and inequalities, Pacific J Optim 12 (2016), pp. 185–206.
   Web of Science ®Google Scholar
• Yuan Liuyang, Cui Fei, Wan Zhongping, Li Weigang, and Wang Wenbo, A nonmonotone smoothing newton method for system of nonlinear inequalities based on a new smoothing function, Comput Appl Math 38 (2) (2019), pp. 91.
   Web of Science ®Google Scholar
• O.L. Mangasarian, Absolute value programming, Comput Optim Appl 36 (1) (2007), pp. 43–53.
   Web of Science ®Google Scholar
• O.L. Mangasarian, A generalized newton method for absolute value equations, Optim Lett 3 (1) (2009), pp. 101–108.
   Web of Science ®Google Scholar
• O.L. Mangasarian and R.R. Meyer, Absolute value equations, Linear Algebra Appl 419 (2–3) (2006), pp. 359–367.
   Web of Science ®Google Scholar
• Amin Mansoori and Majid Erfanian, A dynamic model to solve the absolute value equations, J Comput Appl Math 333 (2018), pp. 28–35.
   Web of Science ®Google Scholar
• Xin-He Miao, Jiantao Yang, and Shenglong Hu, A generalized newton method for absolute value equations associated with circular cones, Appl Math Comput 269 (2015), pp. 155–168.
   Web of Science ®Google Scholar
• Chieu Thanh Nguyen, B. Saheya, Yu-Lin Chang, and Jein-Shan Chen, Unified smoothing functions for absolute value equation associated with second-order cone, Appl Numer Math 135 (2019), pp. 206–227.
   Web of Science ®Google Scholar
• Yigui Ou and Haichan Lin, A hybrid method for solving systems of nonsmooth equations with box constraints, Optim Lett 14 (8) (2020), pp. 2355–2377.
   Web of Science ®Google Scholar
• Oleg Prokopyev, On equivalent reformulations for absolute value equations, Comput Optim Appl 44 (3) (2007), pp. 363.
   Web of Science ®Google Scholar
• Jiri Rohn, A theorem of the alternatives for the equation ax+b|x|=b, Linear Multilinear Algebra 52 (6) (2004), pp. 421–426.
   Web of Science ®Google Scholar
• B. Saheya, Cheng-He Yu, and Jein-Shan Chen, Numerical comparisons based on four smoothing functions for absolute value equation, J Appl Math Comput 56 (1-2) (2018), pp. 131–149.
   Web of Science ®Google Scholar
• B. Saheya, Chieu Thanh Nguyen, and Jein-Shan Chen, Neural network based on systematically generated smoothing functions for absolute value equation, J Appl Math Comput 61 (1–2) (2019), pp. 533–558.
   Web of Science ®Google Scholar
• Ahmet Sahiner, Gulden Kapusuz, and Nurullah Yilmaz, A new smoothing approach to exact penalty functions for inequality constrained optimization problems, Numer Algebra Control Optim 6 (2) (2016), pp. 161–173.
   Google Scholar
• Jingyong Tang and Jinchuan Zhou, A quadratically convergent descent method for the absolute value equation ax+b|x|=b, Oper Res Lett 47 (4) (2019), pp. 229–234.
   Web of Science ®Google Scholar
• Jingyong Tang, Li Dong, Jinchuan Zhou, and Liang Fang, A smoothing newton method for nonlinear complementarity problems, Comput Appl Math 32 (1) (2013), pp. 107–118.
   Web of Science ®Google Scholar
• Pakize Taylan, Gerhard-Wilhelm Weber, and Fatma Yerlikaya Özkurt, A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization, TOP 18 (2) (2010), pp. 377–395.
   Web of Science ®Google Scholar
• Yong Wang and Jian-Xun Zhao, An algorithm for a class of nonlinear complementarity problems with non-lipschitzian functions, Appl Numer Math 82 (2014), pp. 68–79.
   Web of Science ®Google Scholar
• F. Wang, Z. Yu, and C. Gao, A smoothing neural network algorithm for absolute value equations, Engineering 07 (09) (2015), pp. 567–576.
   Google Scholar
• Adilson Elias Xavier, The hyperbolic smoothing clustering method, Pattern Recognit 43 (3) (2010), pp. 731–737.
   Web of Science ®Google Scholar
• Nurullah Yilmaz and Ahmet Sahiner, New smoothing approximations to piecewise smooth functions and applications, Numer Funct Anal Optim 40 (5) (2019), pp. 513–534.
   Web of Science ®Google Scholar
• Nurullah Yilmaz and Ahmet Sahiner, On a new smoothing technique for non-smooth, non-convex optimization, Numer Algebra Control Optim 10 (3) (2020), pp. 317.
   Web of Science ®Google Scholar
• Nurullah Yilmaz, Ahmet Sahiner, and Shehab A Ibrahem, Smoothing approximations to non-smooth functions, J Multidiscip Model Optim 1 (2) (2018), pp. 69–74.
   Google Scholar
• Israel Zang, A smoothing-out technique for min–max optimization, Math Program 19 (1) (1980), pp. 61–77.
   Web of Science ®Google Scholar
• Guanglu Zhou, Louis Caccetta, and Kok Lay Teo, A superlinearly convergent method for a class of complementarity problems with non-Lipschitzian functions, SIAM J Optim 20 (4) (2010), pp. 1811–1827.
   Web of Science ®Google Scholar
• Xi Zhang, Wenling Zhao, Guanglu Zhou, and Wanquan Liu, An accelerated monotonic convergent algorithm for a class of non-Lipschitzian ncp(f) involving an m-matrix, J Comput Appl Math 397 (2021), pp. 113624.
   Web of Science ®Google Scholar