Non-Convex Strong Duality Via Subdifferential

REFERENCES

• A. Barbagallo and A. Maugeri ( 2011 ). Duality theory for the dynamic oligopolistic market equilibrium problem . Optimization 60 : 29 – 52 .
   Web of Science ®Google Scholar
• R. I. Bot , E. R. Csetnek , and A. Moldovan ( 2008 ). Revisiting some duality theorems via the quasirelative interior in convex optimization . J. Optim. Theory Appl. 139 ( 1 ): 67 – 84 .
   Web of Science ®Google Scholar
• H. Brezis ( 1972 ). Problèmes unilatraux . J. Math. Pures Appl. 51 : 1 – 168 .
   Web of Science ®Google Scholar
• J. M. Borwein , V. Jeyakumar , A. S. Lewis , and M. Wolkowicz ( 1988 ). Constrained approximation via convex programming. Preprint. University of Waterloo.
   Google Scholar
• P. Daniele , S. Giuffré , G. Idone , and A. Maugeri ( 2007 ). Infinite dimensional duality and applications . Math. Ann. 339 ( 1 ): 221 – 239 .
   Web of Science ®Google Scholar
• P. Daniele , S. Giuffré , and A. Maugeri ( 2009 ). Remarks on general infinitedimension duality with cone and equality constraints , Commun. Appl. Anal. 13 ( 4 ): 567 – 578 .
   Google Scholar
• P. Daniele , S. Giuffré , A. Maugeri , and F. Raciti (XXXX). Duality Theory and Applications. Preprint.
   Google Scholar
• P. Daniele and S. Giuffré ( 2007 ). General infinite dimensional duality and applications to evolutionary network equilibrium problems . Optim. Lett. 1 : 227 – 243 .
   Web of Science ®Google Scholar
• P. Daniele , G. Idone , and A. Maugeri ( 2003 ) Variational inequalities and the continuum model of transportation problem. Int. J. Nonlinear Sci. Numer. Simul. 4:11–16. .
   Google Scholar
• M. B. Donato ( 2011 ). The infinite dimensional Lagrange multipler rule for convex optimization problems . Journal of Functional Analysis 261 : 2083 – 2093 .
   Web of Science ®Google Scholar
• M. B. Donato , A. Maugeri , M. Milasi , and C. Vitanza ( 2008 ). Duality theory for a dynamic Walrasian pure exchange economy . Pac. J. Optim. 4 : 537 – 547 .
   Web of Science ®Google Scholar
• J. Jahn ( 1996 ). Introduction to the Theory of Non Linear Optimization . Springer-Verlag , Berlin .
   Google Scholar
• G. Idone and A. Maugeri ( 2009 ). Generalized constraints qualification conditions and infinite dimensional duality . Taiwanese J. Math. 13 : 1711 – 1722 .
   Web of Science ®Google Scholar
• A. Maugeri ( 2001 ). Equilibrium problems and variational inequalities. Equilibrium problems: Nonsmooth optimization and variational inequality methods . Nonconvex Optim. Appl. 58 : 187 – 205 .
   Google Scholar
• A. Maugeri and D. Puglisi ( 2014 ). A new necessary and sufficient condition for the strong duality and the infinite dimensional Lagrange multiplier rule . J. Math. Anal. Appl. 415 ( 2 ): 661 – 676 .
   Web of Science ®Google Scholar
• A. Maugeri and F. Raciti ( 2010 ). Remarks on infinite dimensional duality . J. Global Optim. 46 : 581 – 588 .
   Web of Science ®Google Scholar
• R. T. Rockafellar ( 1974 ). Conjugate duality and optimization. Lectures given at the Johns Hopkins University, Baltimore, Md., June, 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 16. Society for Industrial and Applied Mathematics, Philadelphia.
   Google Scholar
• C. Zalinescu ( 2012 ). On the use of the quasi-relative interior in optimization. Preprint.
   Google Scholar
• C. Zalinescu , Personal communication, October 4, 2012.
   Google Scholar