On augmented lagrangians for optimization problems with a single constraint

Journal of Global Optimization

Volumn 28, Issue 2, 2004, Pages 153-173

  Gasimov, R N ^a   Rubinov, A M ^b  

^a ESKISEHIR OSMANGAZI UNIVERSITY   (Turkey)

^b UNIVERSITY OF BALLARAT   (Australia)

Author keywords

Augmented Lagrangians; Lagrange type functions; Supergradient method

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; PROBLEM SOLVING;

AUGMENTED LAGRANGIANS; SUPERGRADIENT METHOD;

OPTIMIZATION;

EID: 1542285815     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000015309.88480.2b     Document Type: Article

References (12)

1. Gasimov, R. N. (2002), Augmented Lagrangian duality and nondifferentiable optimization methods in nonconvex programming, Journal of Global Optimization 24, 187-203.
2. Giannessi, F. (1984), Theorems of the alternative and optimality conditions, J. Optimiz. Theory Appl. 42, 331-365.
3. Huang, X.X. and Yang, X.Q. A unified augmented Lagrangian approach to duality and exact penalization, submitted paper.
4. Rockafellar, R.T. (1974), Augmented Lagrange multiplier functions and duality in nonconvex programming, SIAM Journal on Control and Optimization, 12, 268-285.
5. Rockafellar, R.T. (1993), Lagrange multipliers and optimality, SIAM Review, 35, 183-238.
6. Rockafellar, R. T. and Wets, J.-B. (1998), Variational Analysis, Springer, Berlin, Heidelberg.
7. Rubinov, A. M. (2000), Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht.
8. Rubinov, A.M. and Uderzo, A. (2001), On global optimality conditions via separation functions, J. Optimization Theory and Applications, 109, 345-370.
9. Rubinov, A. M., Glover, B.M. and Yang, X.Q. (1999), Decreasing functions with application to penalization, SIAM Journal Optimization, 10, 289-313.
10. Rubinov, A. M., Glover, B. M. and Yang, X. Q. (1999) Extended Lagrange and penalty functions in continuous optimization, Optimization, 46, 326-351.
11. Rubinov, A.M. and Yang, X.Q. Lagrange-Type Functions in Constrained Non-Convex Optimization, Kluwer Academic Publishers, Dordrecht, (in press).
12. Yang, X.Q. and Huang, X.X. (2001), A nonlinear Lagrangian approach to constrained optimization problems, SIAM Journal Optimization, 14, 1119-1144.