A unified augmented Lagrangian approach to duality and exact penalization

Mathematics of Operations Research

Volumn 28, Issue 3, 2003, Pages 533-552

  Huang, X X ^a   Yang, X Q ^b  

^a CHONGQING NORMAL UNIVERSITY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Constrained program; Duality; Exact penalty function; Generalized augmented Lagrangian; Nonlinear Lagrangian

Indexed keywords

BOUNDARY CONDITIONS; EQUIVALENCE CLASSES; ERROR ANALYSIS; FUNCTION EVALUATION; PROBLEM SOLVING;

LAGRANGIAN DUAL PROBLEM; REAL-VALUED FUNCTION; ZERO DUALITY GAP PROPERTY;

LAGRANGE MULTIPLIERS;

EID: 0141740372     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.28.3.533.16395     Document Type: Article

References (17)

1. Auslender, A. 1999. Penalty and barrier methods: A unified framework. SIAM J. Optim. 10 211-230.
2. ____, R. Cominetti, M. Haddou. 1997. Asymptotical analysis for penalty and barrier methods in convex and linear programming. Math. Oper. Res. 22 43-62.
3. Bestsekas, D. P. 1982. Constrained Optimization and Lagrangian Multiplier Methods. Academic Press, New York.
4. Burke, J. V. 1991a. Calmness and exact penalization. SIAM J. Control and Optim. 29, 493-497.
5. ____. 1991b. An exact penalization viewpoint of constrained optimization. SIAM J. Control and Optim. 29 968-998.
6. Huang, X. X., X. Q. Yang. 2001. Duality and exact penalization for vector optimization via augmented Lagrangian. J. Optim. Theory Appl. 111 615-640.
7. ____, ____. Generalized augmented Lagrangian methods for equality constrained optimization problems. Working paper, Hong Kong Polytechnic University, Hong Kong, China.
8. Ioffe, A. 1979. Necessary and sufficient conditions for a local minimum. 3: Second-order conditions and augmented duality. SIAM J. Control and Optim. 17 266-288.
9. Luo, Z. Q., J. S. Pang. Eds. 2000. Error bounds in mathematical programming. Math. Programming Ser. B. 88(2).
10. ____, ____. D. Ralph. 1996. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, New York.
11. Pang, J. S. 1997. Error bounds in mathematical programming. Math. Programming 79 299-332.
12. Rockafellar, R. T. 1974. Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control and Optim. 12 268-285.
13. ____. 1993. Lagrange multipliers and optimality. SIAM Rev. 35 183-238.
14. ____, R. J.-B. Wets. 1998. Variational Analysis. Springer-Verlag, Berlin.
15. Rubinov, A. M., B. M. Glover, X. Q. Yang. 1999a. Decreasing functions with applications to penalization. SIAM J. Optim. 10(1) 289-313.
16. ____, ____, ____. 1999b. Modified Lagrangian and penalty functions in continuous optimization. Optim. 46 327-351.
17. Yang, X. Q., X. X. Huang. 2001. A nonlinear Lagrangian approach to constrained optimization problems. SIAM J. Optim. 11 1119-1144.