Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 67, Issue 5, 2007, Pages 1359-1373

  Liu, Yong Jin ^a   Zhang, Li Wei ^b  

^a SHANTOU UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Nonlinear second order cone optimization problems; The augmented Lagrangian function; The augmented Lagrangian method

Indexed keywords

LAGRANGE MULTIPLIERS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING;

AUGMENTED LAGRANGIAN FUNCTION; AUGMENTED LAGRANGIAN METHOD; NONLINEAR SECOND-ORDER CONE OPTIMIZATION PROBLEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 34247393327     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.07.022     Document Type: Article

References (18)

1. Alizadeh F., and Goldfarb D. Second-order cone programming. Mathematical Programming 95 (2003) 3-51
2. Arrow K.J., and Solow R.M. Gradient methods for constrained maxima with weakened assumptions. In: Arrow K.J., Hurwicz L., and Uzawa H. (Eds). Studies in Linear and Nonlinear Programming (1958), Stanford University Press, Stanford 165-176
3. Bertsekas D.P. Constrained Optimization and Lagrange Multiplier Methods (1982), Academic Press, New York
4. Bonnans J.F., and Shapiro A. Perturbation Analysis of Optimization Problems (2000), Springer-Verlag, New York
5. Bonnans J.F., and Ramírez H.C. Perturbation analysis of second-order cone programming problems. Mathematical Programming, Series B 104 (2005) 205-227
6. J.D. Buys, Dual algorithms for constrained optimization problems, Ph.D. Thesis, University of Leiden, Leiden, The Netherlands
7. Chen X.D., Sun D., and Sun J. Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems. Computational Optimization and Applications 25 (2003) 39-56
8. Debreu G. Definite and semidefinite quadratic forms. Econometrica 20 (1952) 295-300
9. Faraut U., and Korányi A. Analysis on symmetric cones. Oxford Mathematical Monographs (1994), Oxford University Press, New York
10. Hestences M.R. Multiplier and gradient methods. Journal of Optimization Theory and Applications 4 (1969) 303-320
11. Powell M.J.D. A method for nonlinear constrains in minimization problems. In: Fletcher R. (Ed). Optimization (1969), Academic Press, New York
12. Rockafellar R.T. A dual approach to solving nonlinear programming problems by unconstrained optimization. Mathematical Programming 5 (1973) 354-373
13. Rockafellar R.T. The multiplier method of Hestenes and Powell applied to convex programming. Journal of Optimization Theory and Applications 12 (1973) 555-562
14. Rockafellar R.T. Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM Journal on Control 12 (1974) 268-285
15. Rockafellar R.T., and Wets R.J.-B. Variational Analysis (1998), Springer-Verlag, New York
16. Shapiro A., and Sun J. Some properties of the augmented Lagrangian in cone constrained optimization. Mathematics of Operations Research 29 3 (2004) 479-491
17. D. Sun, J. Sun, L.-W. Zhang, The rate of convergence of the augmented Lagrangian method for semidefinite programming, Department of Mathematics, Mathematical Programming (2006) (in press)
18. J. Sun, L.-W. Zhang, Y. Wu, Some properties of the augmented Lagrangian in nonlinear semidefinite optimization, Journal of Optimization Theory and Applications (in press)