zbMATH — the first resource for mathematics

A novel value for the parameter in the Dai-Liao-type conjugate gradient method. (English) Zbl 1460.65079
Summary: A new rule for calculating the parameter \(t\) involved in each iteration of the MHSDL (Dai-Liao) conjugate gradient (CG) method is presented. The new value of the parameter initiates a more efficient and robust variant of the Dai-Liao algorithm. Under proper conditions, theoretical analysis reveals that the proposed method in conjunction with backtracking line search is of global convergence. Numerical experiments are also presented, which confirm the influence of the new value of the parameter \(t\) on the behavior of the underlying CG optimization method. Numerical comparisons and the analysis of obtained results considering Dolan and Moré’s performance profile show better performances of the novel method with respect to all three analyzed characteristics: number of iterative steps, number of function evaluations, and CPU time.
65K10 Numerical optimization and variational techniques
90C26 Nonconvex programming, global optimization
Full Text: DOI
[1] Dai, Y. -H.; Liao, L. -Z., New conjugacy conditions and related nonlinear conjugate gradient methods, Applied Mathematics and Optimization, 43, 1, 87-101 (2001) · Zbl 0973.65050
[2] Cheng, Y.; Mou, Q.; Pan, X.; Yao, S., A sufficient descent conjugate gradient method and its global convergence, Optimization Methods and Software, 31, 3, 577-590 (2016) · Zbl 1351.90130
[3] Livieris, I. E.; Pintelas, P., A descent Dai-Liao conjugate gradient method based on a modified secant equation and its global convergence, ISRN Computational Mathematics, 2012 (2012) · Zbl 1245.65067
[4] Peyghami, M. R.; Ahmadzadeh, H.; Fazli, A., A new class of efficient and globally convergent conjugate gradient methods in the Dai-Liao family, Optimization Methods and Software, 30, 4, 843-863 (2015) · Zbl 1328.90143
[5] Yabe, H.; Takano, M., Global convergence properties of nonlinear conjugate gradient methods with modified secant condition, Computational Optimization and Applications, 28, 2, 203-225 (2004) · Zbl 1056.90130
[6] Yao, S.; Qin, B., A hybrid of DL and WYL nonlinear conjugate gradient methods, Abstract and Applied Analysis, 2014 (2014) · Zbl 1449.90366
[7] Yao, S.; Lu, X.; Wei, Z., A conjugate gradient method with global convergence for large-scale unconstrained optimization problems, Journal of Applied Mathematics, 2013 (2013) · Zbl 1397.65092
[8] Zheng, Y.; Zheng, B., Two new Dai-Liao-type conjugate gradient methods for unconstrained optimization problems, Journal of Optimization Theory and Applications, 175, 2, 502-509 (2017) · Zbl 1380.65108
[9] Zhou, W.; Zhang, L., A nonlinear conjugate gradient method based on the MBFGS secant condition, Optimization Methods and Software, 21, 5, 707-714 (2006) · Zbl 1112.90096
[10] Hu, W.; Wu, J.; Yuan, G., Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration, Applied Numerical Mathematics, 158, 360-376 (2020) · Zbl 1450.90028
[11] Yuan, G.; Li, T.; Hu, W., A conjugate gradient algorithm for large-scale nonlinear equations and image restoration problems, Applied Numerical Mathematics, 147, 129-141 (2020) · Zbl 1433.90165
[12] Andrei, N., Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization, Bulletin of the Malaysian Mathematical Sciences Society, 34, 2, 319-330 (2011) · Zbl 1225.49030
[13] Hager, W. W.; Zhang, H., A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM Journal on Optimization, 16, 1, 170-192 (2005) · Zbl 1093.90085
[14] Hager, W. W.; Zhang, H., Algorithm 851, ACM Transactions on Mathematical Software, 32, 1, 113-137 (2006) · Zbl 1346.90816
[15] Dai, Y. -H.; Kou, C. -X., A nonlinear conjugate gradient algorithm with an optimal property and an improved Wolfe line search, SIAM Journal on Optimization, 23, 1, 296-320 (2013) · Zbl 1266.49065
[16] Babaie-Kafaki, S.; Ghanbari, R., The Dai-Liao nonlinear conjugate gradient method with optimal parameter choices, European Journal of Operational Research, 234, 3, 625-630 (2014) · Zbl 1304.90216
[17] Andrei, N., A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues, Numerical Algorithms, 77, 4, 1273-1282 (2018) · Zbl 06860411
[18] Lotfi, M.; Hosseini, S. M., An efficient Dai-Liao type conjugate gradient method by reformulating the CG parameter in the search direction equation, Journal of Computational and Applied Mathematics, 371, article 112708 (2020) · Zbl 07169526
[19] Li, X.; Ruan, Q., A modified PRP conjugate gradient algorithm with trust region for optimization problems, Numerical Functional Analysis and Optimization, 32, 5, 496-506 (2011) · Zbl 1230.65068
[20] Andrei, N., An acceleration of gradient descent algorithm with backtracking for unconstrained optimization, Numerical Algorithms, 42, 1, 63-73 (2006) · Zbl 1101.65058
[21] Stanimirovic, P. S.; Miladinovic, M. B., Accelerated gradient descent methods with line search, Numerical Algorithms, 54, 4, 503-520 (2010) · Zbl 1198.65104
[22] Cheng, W., A two-term PRP-based descent method, Numerical Functional Analysis and Optimization, 28, 11-12, 1217-1230 (2007) · Zbl 1138.90028
[23] Zoutendijk, G.; Abadie, J., Nonlinear programming, computational methods, Integer and Nonlinear Programming, North-Holland, 37-86 (1970), Amsterdam: North-Holland, Amsterdam
[24] Andrei, N., An unconstrained optimization test functions collection, Advanced Modeling and Optimization, 10, 1, 147-161 (2008) · Zbl 1161.90486
[25] Bongartz, I.; Conn, A. R.; Gould, N.; Toint, P. L., CUTE: constrained and unconstrained testing environments, ACM Transactions on Mathematical Software, 21, 1, 123-160 (1995) · Zbl 0886.65058
[26] Dolan, E. D.; Moré, J. J., Benchmarking optimization software with performance profiles, Mathematical Programming, 91, 2, 201-213 (2002) · Zbl 1049.90004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.