Separation of Nonconvex Sets with General Augmenting Functions

Published Online:https://doi.org/10.1287/moor.1070.0296

References

  • Auslender A., Teboulle M.Asymptotic Cones and Functions in Optimization and Variational Inequalities (2003) (Springer-Verlag, New York) Google Scholar
  • Auslender A., Cominetti R., Haddou M. Asymptotic analysis for penalty and barrier methods in convex and linear programming. Math. Oper. Res. (1997) 22:43–62LinkGoogle Scholar
  • Ben-Tal A., Zibulevski M. Penalty/barrier multiplier methods: A new class of augmented Lagrangian algorithms for large-scale convex prorgramming problems. (1993) . Technical Report 4/93, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa, IsraelGoogle Scholar
  • Bertsekas D. P., Nedić A., Ozdaglar A. Min common/max crossing duality: A simple geometric framework for convex optimization and minimax theory. (2002) . Technical Report LIDS-P-2536, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
  • Bertsekas D. P., Nedić A., Ozdaglar A.Convex Analysis and Optimization (2003) (Athena Scientific, Belmont, MA) Google Scholar
  • Borwein J. M., Lewis A. S.Convex Analysis and Nonlinear Optimization (2000) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Hiriart-Urruty J.-B., Lemarechal C.Convex Analysis and Minimization Algorithms (1993) I and II(Springer-Verlag, Berlin/New York) CrossrefGoogle Scholar
  • Huang X. X., Yang X. Q. A unified augmented Lagrangian approach to duality and exact penalization. Math. Oper. Res. (2003) 28:533–552LinkGoogle Scholar
  • Luenberger D. G.Linear and Nonlinear Programming (2004) 2nd ed.(Kluwer Academic Publishers, Norwell, MA) Google Scholar
  • Nedić A., Ozdaglar A. A geometric framework for nonconvex optimization duality using augmented Lagrangian functions. J. Global Optim. (2008) 40(4):545–573CrossrefGoogle Scholar
  • Polyak B. T.Introduction to Optimization (1987) (Optimization Software Inc., New York) Google Scholar
  • Polyak R. Modified barrier functions: Theory and methods. Math. Programming (1992) 54:177–222CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Rubinov A. M., Yang X. Q.Lagrange-Type Functions in Constrained Nonconvex Optimization (2003) (Kluwer Academic Publishers, Norwell, MA) CrossrefGoogle Scholar
  • Rubinov A. M., Huang X. X., Yang X. Q. The zero duality gap property and lower semicontinuity of the perturbation function. Math. Oper. Res. (2002) 27:775–791LinkGoogle Scholar
  • Tseng P., Bertsekas D. P. On the convergence of the exponential multiplier method for convex programming. Math. Programming (1993) 60:1–19CrossrefGoogle Scholar
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