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Original Articles

Approximate optimality conditions and stopping criteria in canonical DC programming

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Pages 19-27 | Received 19 Dec 2008, Published online: 16 Oct 2009

References

  • Al-Khayyal , F. and Sherali , H. 2000 . On finitely terminating branch-and-bound algorithms for some global optimization problems . SIAM J. Optim. , 10 : 1049 – 1057 .
  • Androulakis , I. , Maranas , C. and Floudas , C. 1995 . α–BB: A global optimization method for general constrained nonconvex problems . J. Global Optim. , 7 : 337 – 363 .
  • Bigi , G. , Frangioni , A. and Zhang , Q. Outer approximation algorithms for canonical DC problems . J. Global Optim. , DOI 10.1007/s10898-009-9415-1
  • Chapelle , O. , Sindhwani , V. and Keerthi , S. S. 2008 . Optimization techniques for semi-supervised support vector machines . J. Mach. Learn. Res. , 9 : 203 – 233 .
  • Fulop , J. 1990 . A finite cutting plane method for solving linear programs with an additional reverse constraint . Eur. J. Oper. Res. , 44 : 395 – 409 .
  • Grippo , L. and Sciandrone , M. 2000 . On the convergence of the block nonlinear Gauss–Seidel method under convex constraints . Oper. Res. Lett. , 26 : 127 – 136 .
  • Nghia , M. D. and Hieu , N. D. 1986 . A method for solving reverse convex programming problems . Acta Math. Vietnam. , 11 : 241 – 252 .
  • Pham , D. T. and El Bernoussi , S. 1989 . Numerical methods for solving a class of global nonconvex optimization problems . Internat. Ser. Numer. Math. , 87 : 97 – 132 .
  • Rikun , A. D. 1997 . A convex envelope formula for multilinear functions . J. Global Optim. , 10 : 425 – 437 .
  • Rockafellar , R. T. 1970 . Convex Analysis , Princeton : Princeton University Press .
  • Ryoo , H. and Sahinidis , N. 2003 . Global optimization of multiplicative programs . J. Global Optim. , 26 : 387 – 418 .
  • Thach , P. T. 1985 . Convex programs with several additional reverse convex constraints . Acta Math. Vietnam. , 10 : 35 – 57 .
  • Tuy , H. 1986 . “ A general deterministic approach to global optimization via d.c. programming ” . In FERMAT Days 85: Mathematics for Optimization , Edited by: Hiriart-Urruty , J. B. 273 – 303 . Amsterdam : North-Holland .
  • Tuy , H. 1987 . Convex programs with an additional reverse convex constraint . J. Optim. Theory Appl. , 52 : 463 – 486 .
  • Tuy , H. 1992 . On nonconvex optimization problems with separated nonconvex variables . J. Global Optim. , 2 : 133 – 144 .
  • Tuy , H. 1995 . Canonical DC programming problem: outer approximation methods revisited . Oper. Res. Lett. , 18 : 99 – 106 .
  • Tuy , H. 1995 . “ D.C. optimization: Theory, methods and algorithms ” . In Handbook of Global Optimization , Edited by: Horst , R. and Pardalos , P. M. 149 – 216 . Dordrecht : Kluwer Academic Publishers .
  • Tuy , H. 1998 . Convex analysis and global optimization , Dordrecht : Kluwer Academic Publishers .
  • Tuy , H. 2005 . Robust solution of nonconvex global optimization problems . J. Global Optim. , 32 : 307 – 323 .
  • Tuy , H. and Tam , B. T. 1995 . Polyhedral annexation vs outer approximation for the decomposition of monotonic quasiconcave minimization problems . Acta Math. Vietnam. , 20 : 99 – 114 .
  • Wen , Y.-W. , Ng , M. K. and Huang , Y.-M. 2008 . Efficient total variation minimization methods for color image restoration . IEEE Trans. Image Process. , 17 : 2081 – 2088 .

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