A descent algorithm without line search for unconstrained optimization
Pages 2528 - 2533
Abstract
In this paper, a new descent algorithm for solving unconstrained optimization problem is presented. Its search direction is descent and line search procedure can be avoided except for the first iteration. It is globally convergent under mild conditions. The search direction of the new algorithm is generalized and convergence of corresponding algorithm is also proved. Numerical results show that the algorithm is efficient for given test problems.
References
[1]
Dai, Y.H. and Yuan, Y., Nonlinear Conjugate Gradient Methods (in Chinese). 2000. Shanghai Science and Technology Press of China, Shanghai.
[2]
Optimization Theory and Methods: Nonlinear Programming. 2006. Springer-Verlag, New York.
[3]
Shi, Z.J. and Shen, J., Convergence of descent method without line search. Appl. Math. Computat. v167. 94-107.
[4]
Barzilai, J. and Borwein, J.M., Two point step size gradient methods. IMA J. Numer. Anal. v8. 141-148.
[5]
Dixon, L.C.W., Conjugate directions without line searches. J. Inst. Math. Appl. v11. 317-328.
[6]
Dai, Y.H. and Yuan, Y., Alternate minimization gradient method. IMA J. Numer. Anal. v23. 377-393.
[7]
Dai, Y.H., Yuan, Y.J. and Yuan, Y., Modified two-point stepsize gradient methods for unconstrained optimization. Computat. Optimizat. Appl. v22. 103-109.
[8]
Dai, Y.H. and Liao, L.Z., R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. v22. 1-10.
[9]
Dai, Y.H. and Zhang, H., An adaptive two-point stepsize gradient algorithm. Numer. Algorithm. v27. 377-385.
[10]
Liu, W.B. and Dai, Y.H., Minimization algorithms based on supervisor and searcher cooperation. JOTA. v111. 359-379.
[11]
Raydan, M., The Barzilai and Borwein method for the large scale unconstrained minimization problem. SIAM J. Optimizat. v7. 26-33.
[12]
Raydan, M., On the Barzilai and Borwein gradient choice of steplength for the gradient method. IMA J. Numer. Anal. v13. 321-326.
[13]
Varhatis, M.N., Amdroulakis, G.S. and Lambrinos, J.N., A class of gradient unconstrained minimization algorithms with adaptive stepsize. J. Comput. Appl. Math. v114. 367-386.
[14]
Low storage methods for unconstrained optimization. Lect. Appl. Math. (AMS). v25. 165-179.
[15]
Birgin, E.G., Martinez, J.M. and Raydan, M., Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. v10. 1196-1211.
[16]
Friedlander, A., Martinez, J.M., Molina, B. and Raydan, M., Gradient method with retards and generalizations. SIAM J. Numer. Anal. v36. 275-289.
[17]
Magoulas, G.D., A class of gradient unconstrained minimization algorithms with adaptive stepsize. J. Comput. Appl. Math. v114. 367-386.
[18]
Glunt, W., Haydan, T.L. and Raydan, M., Molecular conformations from distance matrices. J. Comput. Chem. v14. 114-120.
[19]
Birgin, E.G., Chambouleyron, I. and Martinez, J.M., Estimation of the optical constants and the thickness of thin films using unconstrained optimization. J. Comput. Phys. v151. 862-880.
[20]
Chen, X.D. and Sun, J., Global convergence of a two-parameter family of conjugate gradient methods without line search. J. Computat. Appl. Math. v146. 37-45.
[21]
Sun, J. and Zhang, J.P., Global convergence of conjugate gradient methods without line search. Ann. Operat. Res. v103. 161-173.
[22]
Shi, Z.J., Convergence of line search methods for unconstrained optimization. Appl. Math. Computat. v157. 393-405.
[23]
Shi, Z.J. and Shen, J., A new descent algorithm with curve search rule. Appl. Math. Computat. v161. 753-768.
[24]
Nocedal, J. and Stephen, J.W., Numerical Optimization. 1999. Springer-Verlag, New York.
[25]
Moré, J.J., Garbow, B.S. and Hillstrom, K.E., Testing unconstrained optimization software. ACM Trans. Math. Software. v7. 17-41.
- A descent algorithm without line search for unconstrained optimization
Recommendations
The revised DFP algorithm without exact line search
In this paper, we discuss the convergence of the DFP algorithm with revised search direction. Under some inexact line searches, we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of ...
Memory gradient method with Goldstein line search
In this paper, we present a multi-step memory gradient method with Goldstein line search for unconstrained optimization problems and prove its global convergence under some mild conditions. We also prove the linear convergence rate of the new method ...
Sufficient descent directions in unconstrained optimization
Descent property is very important for an iterative method to be globally convergent. In this paper, we propose a way to construct sufficient descent directions for unconstrained optimization. We then apply the technique to derive a PSB (Powell-...
Comments
Information & Contributors
Information
Published In
Copyright © Elsevier Inc. © 2009.
Publisher
Elsevier Science Inc.
United States
Publication History
Published: 01 December 2009
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 23 Jan 2025