# American Institute of Mathematical Sciences

• Previous Article
On the partial path protection scheme for WDM optical networks and polynomial time computability of primary and secondary paths
• JIMO Home
• This Issue
• Next Article
A quadratically convergent method for minimizing a sum of Euclidean norms with linear constraints
October  2007, 3(4): 645-654. doi: 10.3934/jimo.2007.3.645

## A relaxed extragradient-like method for a class of constrained optimization problem

 1 Institute of Operations Research, Qufu Normal University, Shandong, 276826, China 2 Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R., China

Received  September 2006 Revised  April 2007 Published  October 2007

This paper presents a relaxed extragradient-like method for solving the convexly constrained minimization with optimal value zero. The method is a combination of the extragradient-like algorithm and a halfspace-relaxation technique to the constrained set of the problem. Each iteration of the proposed method consists of the projection onto a halfspace containing the given closed convex set. The method is implemented very easily and is proven to be fully convergent to the solution. Preliminary computational experience is also reported.
Citation: Biao Qu, Naihua Xiu. A relaxed extragradient-like method for a class of constrained optimization problem. Journal of Industrial & Management Optimization, 2007, 3 (4) : 645-654. doi: 10.3934/jimo.2007.3.645
 [1] Luchuan Ceng, Qamrul Hasan Ansari, Jen-Chih Yao. Extragradient-projection method for solving constrained convex minimization problems. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 341-359. doi: 10.3934/naco.2011.1.341 [2] Yuan Shen, Wenxing Zhang, Bingsheng He. Relaxed augmented Lagrangian-based proximal point algorithms for convex optimization with linear constraints. Journal of Industrial & Management Optimization, 2014, 10 (3) : 743-759. doi: 10.3934/jimo.2014.10.743 [3] Kareem T. Elgindy. Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted gegenbauer integral pseudospectral method. Journal of Industrial & Management Optimization, 2018, 14 (2) : 473-496. doi: 10.3934/jimo.2017056 [4] Igor Griva, Roman A. Polyak. Proximal point nonlinear rescaling method for convex optimization. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 283-299. doi: 10.3934/naco.2011.1.283 [5] Nobuko Sagara, Masao Fukushima. trust region method for nonsmooth convex optimization. Journal of Industrial & Management Optimization, 2005, 1 (2) : 171-180. doi: 10.3934/jimo.2005.1.171 [6] Dan Li, Li-Ping Pang, Fang-Fang Guo, Zun-Quan Xia. An alternating linearization method with inexact data for bilevel nonsmooth convex optimization. Journal of Industrial & Management Optimization, 2014, 10 (3) : 859-869. doi: 10.3934/jimo.2014.10.859 [7] Foxiang Liu, Lingling Xu, Yuehong Sun, Deren Han. A proximal alternating direction method for multi-block coupled convex optimization. Journal of Industrial & Management Optimization, 2019, 15 (2) : 723-737. doi: 10.3934/jimo.2018067 [8] Yekini Shehu, Olaniyi Iyiola. On a modified extragradient method for variational inequality problem with application to industrial electricity production. Journal of Industrial & Management Optimization, 2019, 15 (1) : 319-342. doi: 10.3934/jimo.2018045 [9] Ahmet Sahiner, Nurullah Yilmaz, Gulden Kapusuz. A novel modeling and smoothing technique in global optimization. Journal of Industrial & Management Optimization, 2019, 15 (1) : 113-130. doi: 10.3934/jimo.2018035 [10] Tomáš Roubíček. On certain convex compactifications for relaxation in evolution problems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 467-482. doi: 10.3934/dcdss.2011.4.467 [11] Jean-François Babadjian, Clément Mifsud, Nicolas Seguin. Relaxation approximation of Friedrichs' systems under convex constraints. Networks & Heterogeneous Media, 2016, 11 (2) : 223-237. doi: 10.3934/nhm.2016.11.223 [12] Murat Adivar, Shu-Cherng Fang. Convex optimization on mixed domains. Journal of Industrial & Management Optimization, 2012, 8 (1) : 189-227. doi: 10.3934/jimo.2012.8.189 [13] Yigui Ou, Yuanwen Liu. A memory gradient method based on the nonmonotone technique. Journal of Industrial & Management Optimization, 2017, 13 (2) : 857-872. doi: 10.3934/jimo.2016050 [14] Guanglu Zhou. A quadratically convergent method for minimizing a sum of Euclidean norms with linear constraints. Journal of Industrial & Management Optimization, 2007, 3 (4) : 655-670. doi: 10.3934/jimo.2007.3.655 [15] Zhichuan Zhu, Bo Yu, Li Yang. Globally convergent homotopy method for designing piecewise linear deterministic contractual function. Journal of Industrial & Management Optimization, 2014, 10 (3) : 717-741. doi: 10.3934/jimo.2014.10.717 [16] Vadim Azhmyakov. An approach to controlled mechanical systems based on the multiobjective optimization technique. Journal of Industrial & Management Optimization, 2008, 4 (4) : 697-712. doi: 10.3934/jimo.2008.4.697 [17] Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems & Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099 [18] Yong Xia, Yu-Jun Gong, Sheng-Nan Han. A new semidefinite relaxation for $L_{1}$-constrained quadratic optimization and extensions. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 185-195. doi: 10.3934/naco.2015.5.185 [19] Anulekha Dhara, Aparna Mehra. Conjugate duality for generalized convex optimization problems. Journal of Industrial & Management Optimization, 2007, 3 (3) : 415-427. doi: 10.3934/jimo.2007.3.415 [20] Yong Wang, Wanquan Liu, Guanglu Zhou. An efficient algorithm for non-convex sparse optimization. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2018134

2017 Impact Factor: 0.994