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Journal articles on the topic 'Generalized trust region subproblem'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Pong, Ting Kei, and Henry Wolkowicz. "The generalized trust region subproblem." Computational Optimization and Applications 58, no. 2 (January 17, 2014): 273–322. http://dx.doi.org/10.1007/s10589-013-9635-7.

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2

Jia, Zhongxiao, and Fa Wang. "The Convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem." SIAM Journal on Optimization 31, no. 1 (January 2021): 887–914. http://dx.doi.org/10.1137/19m1279691.

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3

Adachi, Satoru, Satoru Iwata, Yuji Nakatsukasa, and Akiko Takeda. "Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem." SIAM Journal on Optimization 27, no. 1 (January 2017): 269–91. http://dx.doi.org/10.1137/16m1058200.

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4

Salahi, M., and A. Taati. "An efficient algorithm for solving the generalized trust region subproblem." Computational and Applied Mathematics 37, no. 1 (May 13, 2016): 395–413. http://dx.doi.org/10.1007/s40314-016-0349-1.

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5

Jiang, Rujun, and Duan Li. "Novel Reformulations and Efficient Algorithms for the Generalized Trust Region Subproblem." SIAM Journal on Optimization 29, no. 2 (January 2019): 1603–33. http://dx.doi.org/10.1137/18m1174313.

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6

Wang, Shu, and Yong Xia. "Strong duality for generalized trust region subproblem: S-lemma with interval bounds." Optimization Letters 9, no. 6 (October 14, 2014): 1063–73. http://dx.doi.org/10.1007/s11590-014-0812-0.

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7

Zhou, Jing, Cheng Lu, Ye Tian, and Xiaoying Tang. "A SOCP relaxation based branch-and-bound method for generalized trust-region subproblem." Journal of Industrial & Management Optimization 17, no. 1 (2021): 151–68. http://dx.doi.org/10.3934/jimo.2019104.

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8

Jin, Qingwei, Shu-Cherng Fang, and Wenxun Xing. "On the global optimality of generalized trust region subproblems." Optimization 59, no. 8 (November 2010): 1139–51. http://dx.doi.org/10.1080/02331930902995236.

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9

Jiang, Rujun, and Duan Li. "A Linear-Time Algorithm for Generalized Trust Region Subproblems." SIAM Journal on Optimization 30, no. 1 (January 2020): 915–32. http://dx.doi.org/10.1137/18m1215165.

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10

Jiang, Rujun, Duan Li, and Baiyi Wu. "SOCP reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices." Mathematical Programming 169, no. 2 (April 18, 2017): 531–63. http://dx.doi.org/10.1007/s10107-017-1145-4.

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11

Mei, Xiaojun, Huafeng Wu, Jiangfeng Xian, Bowen Chen, Hao Zhang, and Xia Liu. "A Robust, Non-Cooperative Localization Algorithm in the Presence of Outlier Measurements in Ocean Sensor Networks." Sensors 19, no. 12 (June 16, 2019): 2708. http://dx.doi.org/10.3390/s19122708.

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As an important means of multidimensional observation on the sea, ocean sensor networks (OSNs) could meet the needs of comprehensive information observations in large-scale and multifactor marine environments. In what concerns OSNs, accurate location information is the basis of the data sets. However, because of the multipath effect—signal shadowing by waves and unintentional or malicious attacks—outlier measurements occur frequently and inevitably, which directly degrades the localization accuracy. Therefore, increasing localization accuracy in the presence of outlier measurements is a critical issue that needs to be urgently tackled in OSNs. In this case, this paper proposed a robust, non-cooperative localization algorithm (RNLA) using received signal strength indication (RSSI) in the presence of outlier measurements in OSNs. We firstly formulated the localization problem using a log-normal shadowing model integrated with a first order Taylor series. Nevertheless, the problem was infeasible to solve, especially in the presence of outlier measurements. Hence, we then converted the localization problem into the optimization problem using squared range and weighted least square (WLS), albeit in a nonconvex form. For the sake of an accurate solution, the problem was then transformed into a generalized trust region subproblem (GTRS) combined with robust functions. Although GTRS was still a nonconvex framework, the solution could be acquired by a bisection approach. To ensure global convergence, a block prox-linear (BPL) method was incorporated with the bisection approach. In addition, we conducted the Cramer–Rao low bound (CRLB) to evaluate RNLA. Simulations were carried out over variable parameters. Numerical results showed that RNLA outperformed the other algorithms under outlier measurements, notwithstanding that the time for RNLA computation was a little bit more than others in some conditions.

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12

Zhu, Honglan, and Qin Ni. "A Simple Alternating Direction Method for the Conic Trust Region Subproblem." Mathematical Problems in Engineering 2018 (December 18, 2018): 1–9. http://dx.doi.org/10.1155/2018/5358191.

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A simple alternating direction method is used to solve the conic trust region subproblem of unconstrained optimization. By use of the new method, the subproblem is solved by two steps in a descent direction and its orthogonal direction, the original conic trust domain subproblem into a one-dimensional subproblem and a low-dimensional quadratic model subproblem, both of which are very easy to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that the new method seems simple and effective.

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13

Zhu, Detong. "An affine scaling interior point backtracking algorithm for nonlinear constrained optimisation." ANZIAM Journal 46, no. 1 (July 2004): 45–66. http://dx.doi.org/10.1017/s1446181100013663.

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AbstractIn this paper we propose a new affine scaling interior trust region algorithm with a nonmonotonic backtracking technique for nonlinear equality constrained optimisation with nonnegative constraints on the variables. In order to deal with large problems, the general full trust region subproblem is decomposed into a pair of trust region subproblems in horizontal and vertical subspaces. The horizontal trust region subproblem in the algorithm is defined by minimising a quadratic function subject only to an ellipsoidal constraint in a null tangential subspace and the vertical trust region subproblem is defined by the least squares subproblem subject only to an ellipsoidal constraint. By adopting Fletcher's penalty function as the merit function, combining a trust region strategy and a nonmonotone line search, the mixing technique will switch to a backtracking step generated by the two trust region subproblems to obtain an acceptable step. The global convergence of the proposed algorithm is proved while maintaining a fast local superlinear convergence rate, which is established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some highly nonlinear cases.

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14

Grodzevich, Oleg, and Henry Wolkowicz. "Regularization using a parameterized trust region subproblem." Mathematical Programming 116, no. 1-2 (April 28, 2007): 193–220. http://dx.doi.org/10.1007/s10107-007-0126-4.

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15

Fortin, Charles, and Henry Wolkowicz. "The trust region subproblem and semidefinite programming*." Optimization Methods and Software 19, no. 1 (February 2004): 41–67. http://dx.doi.org/10.1080/10556780410001647186.

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16

Cui, Zhaocheng. "A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization." Journal of Optimization 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/237279.

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We propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

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17

Zhao, Lijuan. "Nonmonotone conic trust region method with line search technique for bound constrained optimization." RAIRO - Operations Research 53, no. 3 (June 24, 2019): 787–805. http://dx.doi.org/10.1051/ro/2017054.

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In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

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18

An, Le Thi Hoai, Pham Dinh Tao, and Dinh Nho Hào. "On the ill-posedness of the trust region subproblem." Journal of Inverse and Ill-posed Problems 11, no. 6 (December 2003): 545–77. http://dx.doi.org/10.1515/156939403322759642.

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19

Salahi, Maziar. "An Iterative Algorithm for the Conic Trust Region Subproblem." International Journal of Applied and Computational Mathematics 3, no. 3 (September 26, 2016): 2553–58. http://dx.doi.org/10.1007/s40819-016-0254-8.

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20

Burer, Samuel, and Boshi Yang. "The trust region subproblem with non-intersecting linear constraints." Mathematical Programming 149, no. 1-2 (February 5, 2014): 253–64. http://dx.doi.org/10.1007/s10107-014-0749-1.

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21

Gould, Nicholas I. M., Stefano Lucidi, Massimo Roma, and Philippe L. Toint. "Solving the Trust-Region Subproblem using the Lanczos Method." SIAM Journal on Optimization 9, no. 2 (January 1999): 504–25. http://dx.doi.org/10.1137/s1052623497322735.

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22

Toint, Philippe L., D. Tomanos, and M. Weber-Mendonça. "A multilevel algorithm for solving the trust-region subproblem." Optimization Methods and Software 24, no. 2 (April 2009): 299–311. http://dx.doi.org/10.1080/10556780802571467.

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23

Bergmann, Ørjan, and Trond Steihaug. "Solving trust-region subproblem augmented with linear inequality constraints." Optimization Methods and Software 28, no. 1 (February 2013): 26–36. http://dx.doi.org/10.1080/10556788.2011.582501.

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24

Zhang, Lei-Hong, and Chungen Shen. "A Nested Lanczos Method for the Trust-Region Subproblem." SIAM Journal on Scientific Computing 40, no. 4 (January 2018): A2005—A2032. http://dx.doi.org/10.1137/17m1145914.

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25

Zhang, Leihong, Weihong Yang, Chungen Shen, and Jiang Feng. "Error bounds of Lanczos approach for trust-region subproblem." Frontiers of Mathematics in China 13, no. 2 (March 3, 2018): 459–81. http://dx.doi.org/10.1007/s11464-018-0687-y.

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26

Salahi, M., and S. Fallahi. "Trust region subproblem with an additional linear inequality constraint." Optimization Letters 10, no. 4 (October 5, 2015): 821–32. http://dx.doi.org/10.1007/s11590-015-0957-5.

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27

Yuan, Gonglin, Shide Meng, and Zengxin Wei. "A Trust-Region-Based BFGS Method with Line Search Technique for Symmetric Nonlinear Equations." Advances in Operations Research 2009 (2009): 1–22. http://dx.doi.org/10.1155/2009/909753.

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A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method.

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28

Zhang, De Qing, Pei Pei Zhou, and Qing Hua Zhou. "A New Hybrid Algorithm of Trust Region Methods." Applied Mechanics and Materials 680 (October 2014): 442–46. http://dx.doi.org/10.4028/www.scientific.net/amm.680.442.

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In the solution of trust region subproblem within the classical trust region algorithms, the centre of sphere is the current interaction point and one step-size is the upper bound. Considering that only with the negative gradient direction to acute angle may reduce the function value, we introduce the parameter to control of the centre of sphere and the radius. Based on the numerical experiments, obtains the value range of the parameter. The numerical evaluation demonstrates the validity of the new trust region algorithms.

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29

Zhu, Honglan, Qin Ni, Liwei Zhang, and Weiwei Yang. "A Fractional Trust Region Method for Linear Equality Constrained Optimization." Discrete Dynamics in Nature and Society 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/8676709.

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A quasi-Newton trust region method with a new fractional model for linearly constrained optimization problems is proposed. We delete linear equality constraints by using null space technique. The fractional trust region subproblem is solved by a simple dogleg method. The global convergence of the proposed algorithm is established and proved. Numerical results for test problems show the efficiency of the trust region method with new fractional model. These results give the base of further research on nonlinear optimization.

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30

Oruh, B. I. "A New Dogleg Method for Solving the Trust-Region Subproblem." IOSR Journal of Mathematics 8, no. 2 (2013): 41–48. http://dx.doi.org/10.9790/5728-0824148.

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31

Yang, Boshi, and Samuel Burer. "A Two-Variable Approach to the Two-Trust-Region Subproblem." SIAM Journal on Optimization 26, no. 1 (January 2016): 661–80. http://dx.doi.org/10.1137/130945880.

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32

Heinkenschloss, M. "On the solution of a two ball trust region subproblem." Mathematical Programming 64, no. 1-3 (March 1994): 249–76. http://dx.doi.org/10.1007/bf01582576.

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33

Yuan, Y. "On a subproblem of trust region algorithms for constrained optimization." Mathematical Programming 47, no. 1-3 (May 1990): 53–63. http://dx.doi.org/10.1007/bf01580852.

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34

Tao, Pham Dinh, and Le Thi Hoai An. "A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem." SIAM Journal on Optimization 8, no. 2 (May 1998): 476–505. http://dx.doi.org/10.1137/s1052623494274313.

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35

Song, Liqiang, and Wei Hong Yang. "A Block Lanczos Method for the Extended Trust-Region Subproblem." SIAM Journal on Optimization 29, no. 1 (January 2019): 571–94. http://dx.doi.org/10.1137/17m1156617.

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36

Le Thi, Hoai An, Tao Pham Dinh, and Nguyen Dong Yen. "Behavior of DCA sequences for solving the trust-region subproblem." Journal of Global Optimization 53, no. 2 (March 10, 2011): 317–29. http://dx.doi.org/10.1007/s10898-011-9696-z.

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37

Ji, Ying, Tienan Wang, and Yijun Li. "A Continuous Trust-Region-Type Method for Solving Nonlinear Semidefinite Complementarity Problem." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/589731.

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We propose a new method to solve nonlinear semidefinite complementarity problem by combining a continuous method and a trust-region-type method. At every iteration, we need to calculate a second-order cone subproblem. We show the well-definedness of the method. The global convergent result is established.

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38

Beck, Amir, and Yakov Vaisbourd. "Globally Solving the Trust Region Subproblem Using Simple First-Order Methods." SIAM Journal on Optimization 28, no. 3 (January 2018): 1951–67. http://dx.doi.org/10.1137/16m1150281.

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39

Tran, Van Nghi. "Coderivatives Related to Parametric Extended Trust Region Subproblem and Their Applications." Taiwanese Journal of Mathematics 22, no. 2 (April 2018): 485–511. http://dx.doi.org/10.11650/tjm/170907.

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40

Wang, JianYu, and Qin Ni. "An algorithm for solving new trust region subproblem with conic model." Science in China Series A: Mathematics 51, no. 3 (March 2008): 461–73. http://dx.doi.org/10.1007/s11425-007-0149-6.

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41

Kearsley, Anthony J. "Matrix-free algorithm for the large-scale constrained trust-region subproblem." Optimization Methods and Software 21, no. 2 (April 2006): 233–45. http://dx.doi.org/10.1080/10556780500094754.

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42

Rezaee, Saeed, and Saman Babaie-Kafaki. "An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems." RAIRO - Operations Research 53, no. 3 (June 25, 2019): 829–39. http://dx.doi.org/10.1051/ro/2017057.

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Based on a modified secant equation, we propose a scalar approximation of the Hessian to be used in the trust region subproblem. Then, we suggest an adaptive nonmonotone trust region algorithm with a simple quadratic model. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan-Moré performance profile. They demonstrate efficiency of the proposed algorithm.

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43

Anstreicher, Kurt M. "Kronecker Product Constraints with an Application to the Two-Trust-Region Subproblem." SIAM Journal on Optimization 27, no. 1 (January 2017): 368–78. http://dx.doi.org/10.1137/16m1078859.

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44

Lu, Zhaosong, and Renato D. C. Monteiro. "A modified nearly exact method for solving low-rank trust region subproblem." Mathematical Programming 109, no. 2-3 (November 22, 2006): 385–411. http://dx.doi.org/10.1007/s10107-006-0025-0.

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45

Rojas, Marielba, Sandra A. Santos, and Danny C. Sorensen. "A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem." SIAM Journal on Optimization 11, no. 3 (January 2001): 611–46. http://dx.doi.org/10.1137/s105262349928887x.

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46

Apostolopoulou, M. S., D. G. Sotiropoulos, and P. Pintelas. "Solving the quadratic trust-region subproblem in a low-memory BFGS framework." Optimization Methods and Software 23, no. 5 (October 2008): 651–74. http://dx.doi.org/10.1080/10556780802413579.

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47

Fortin, Charles. "Computing the Local-Nonglobal Minimizer of a Large Scale Trust-Region Subproblem." SIAM Journal on Optimization 16, no. 1 (January 2005): 263–96. http://dx.doi.org/10.1137/030602290.

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48

Tuan, Hoang Ngoc, and Nguyen Dong Yen. "Convergence of Pham Dinh–Le Thi’s algorithm for the trust-region subproblem." Journal of Global Optimization 55, no. 2 (December 21, 2011): 337–47. http://dx.doi.org/10.1007/s10898-011-9820-0.

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49

Wu, C. W., J. P. Cao, and L. F. Wang. "Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems." Mathematical Problems in Engineering 2020 (June 19, 2020): 1–9. http://dx.doi.org/10.1155/2020/2539196.

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For solving nonlinear complementarity problems, a new algorithm is proposed by using multidimensional filter techniques and a trust-region method. The algorithm is shown to be globally convergent under the reasonable assumptions and does not depend on any extra restoration procedure. In particular, it shows that the subproblem is a convex quadratic programming problem, which is easier to be solved. The results of numerical experiments show its efficiency.

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50

Weiwei, Yang, Yang Yueting, Zhang Chenhui, and Cao Mingyuan. "A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/478407.

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We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.

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