The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function

References

• Balder E. J. An extension of duality-stability relations to non-convex optimization problems. SIAM J. Control Optim. (1997) 15:329–343Crossref, Google Scholar
• Bertsekas D. P.Constrained optimization and Lagrangian multiplier methods (1982) (Academic Press, New York) Google Scholar
• Dolecki S., Kurcyusz S. On Φ-convexity in extremal problems. SIAM J. Control Optim. (1978) 16:277–300Crossref, Google Scholar
• Golshtein E. G., Tretyakov N. V.Modified Lagrangians and monotone maps in optimization (1996) (John Wiley, New York) Google Scholar
• Goh C. J., Yang X. Q. A nonlinear Lagrangian theory for nonconvex optimization. J. Optim. Theory Appl. (2001) 109(1):99–121Crossref, Google Scholar
• Huang X. X., Yang X. Q. A unified augmented Lagrangian approach to duality and exact penalization. (2002) . Working paper. Hong Kong Polytechnic University, Hong KongGoogle Scholar
• Kutateladze S. S., Rubinov A. M. Minkowski duality and its applications. Russian Math. Surveys (1972) 27:137–191Crossref, Google Scholar
• Lindberg P. O., Prekopa A. A generalization of Fenchel conjugation giving generalized Lagrangians and symmetric noncovex duality. Survey of Mathematical Programming, 1 (1979) (North-Holland, Amsterdam, The Netherlands) 249–267Google Scholar
• Luo Z. Q., Pang J. S., Ralph D.Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, New York) Crossref, Google Scholar
• Penot J. P. Augmented Lagrangians, duality and growth conditions. (2001) . Working paper. University of Pau, Pau, FranceGoogle Scholar
• Pallaschke D., Rolewicz S.Foundation of Mathematical Optimization (1997) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Rockafellar R. T. Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control Optim. (1947) 12:268–285Crossref, Google Scholar
• Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer-Verlag, Berlin) Crossref, Google Scholar
• Rubinov A. M.Abstract Convexity and Global Optimization (2000) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Rubinov A. M., Glover B. M. Duality for increasing positively homogeneous functions and normal sets. Recherche Operationnelle/Oper. Res. (1998) 32:105–123Google Scholar
• Rubinov A. M., Glover B. M., Yang X. Q. Decreasing functions with applications to penalization. SIAM J. Optim. (1999) 10(1):289–313Crossref, Google Scholar
• Rubinov A. M., Glover B. M., Yang X. Q. Modified Lagrangian and penalty functions in continuous optimization. Optimization (1999) 46:327–351Crossref, Google Scholar
• Singer I.Abstract Convex Analysis (1997) (Wiley-Interscience Publication, New York) Google Scholar
• Yang X. Q., Huang X. X. A nonlinear Lagrangian approach to constrained optimization problems. SIAM J. Optim. (2001) 14:1119–1144Crossref, Google Scholar