A Unified Augmented Lagrangian Approach to Duality and Exact Penalization

References

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