Abstract
In this paper, we introduce a new notion of augmenting function known as indicator augmenting function to establish a minmax type duality relation, existence of a path of solution converging to optimal value and a zero duality gap relation for a nonconvex primal problem and the corresponding Lagrangian dual problem. We also obtain necessary and sufficient conditions for an exact penalty representation in the framework of indicator augmented Lagrangian.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Auslender A.: Penalty and barrier methods: a unified framework. SIAM J. Optim. 10, 211–230 (1999). doi:10.1137/S1052623497324825
Huang X.X., Yang X.Q.: A unified augmented Lagrangian approach to duality and exact penalization. Math. Oper. Res. 28, 533–552 (2003). doi:10.1287/moor.28.3.533.16395
Nedic A., Ozdaglar A.: A geometric framework for nonconvex optimization duality using augmented Lagrangian functions. J. Glob. Optim. 40, 545–573 (2008). doi:10.1007/s10898-006-9122-0
Rubinov A.M., Huang X.X., Yang X.Q.: The zero duality gap property and lower semicontinuity of the perturbation function. Math. Oper. Res. 27, 775–791 (2002). doi:10.1287/moor.27.4.775.295
Rubinov A.M.: Abstract Convexity and Global Optimization. Kluwer, Dordrecht (2000)
Rubinov A.M., Yang X.Q.: Lagrange-type Functions in Constrained Nonconvex Optimization. Kluwer, Massachusetts (2003)
Rockafellar R.T.: Augmented Lagrangian multiplier functions and duality in nonconvex programming. SIAM J. Contr. Optim. 12, 268–285 (1974). doi:10.1137/0312021
Rockafellar R.T.: Lagrangian multipliers and optimality. SIAM Rev. 35, 183–238 (1993). doi:10.1137/1035044
Rockafellar R.T., Wets R.J.-B.: Variational Analysis. Springer, Berlin (1998)
Yang X.Q., Huang X.X.: A nonlinear Lagrangian approach to constrained optimization problems. SIAM J. Optim. 11, 1119–1144 (2001). doi:10.1137/S1052623400371806
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lalitha, C.S. A new augmented Lagrangian approach to duality and exact penalization. J Glob Optim 46, 233–245 (2010). https://doi.org/10.1007/s10898-009-9420-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9420-4