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The Properties of The Weak Subdifferentials. . .

Year 2010, Volume: 23 Issue: 1, 49 - 52, 08.03.2010

Abstract

This paper deals with the weak subdifferentials. The properties of the weak subdifferentials are examined. It is showed that the weak subdifferential of a function having a global minimum is not empty.


Key Words: Subdifferential, Weak subgradient, Weak subdifferential.

 

References

  • Aubin, J-P., Ekeland, I., “Applied Nonlinear Analysis”, Wiley-İnterscience, New York, USA, 159-200 (1984).
  • Azimov, A. Y., Gasimov R. N., “On weak conjugacy, weak subdifferentials and duality with zero International Journal of Applied Mathematics, 1:171-192 (1999). optimization”,
  • Azimov, A. Y., Gasimov R. N., “Stability and duality of nonconvex problems via augmented lagrangian”, Cybenetics and Systems Analysis, 38:412-421 (2002).
  • Clarke F.H., “A new approach to lagrange multipliers”, Mathematics Operations Research, 1:165-174 (1976).
  • Clarke F.H., “Optimization and Nonsmooth Analysis”, Wiley-İnterscience, New York, USA, 9-30 (1983).
  • Ekeland I., Temam R., “Convex Analysis and Variational Problems”, Elsevier Norht-Holland, Amsterdam, 3-34 (1983).
  • Rocafellar R. T., “Convex Analysis”, Princeton University, New Jersey, USA, 215-227 (1970).
  • Kasımbeyli R. N., “Radial Epiderivatives and Set Valued Optimization”, Optimization, 58(5):521- 534 (2009).
  • Rocafellar R. T., “Proximal subgradients, marginal values and augmented lagrangian in nonconvex optimization”, Math. Oper. Res., 6:427-437, (1981).
  • Rocafellar R. T., “Lagrange multipliers and optimality”, SIAM Review, 35:183-238 (1993).
Year 2010, Volume: 23 Issue: 1, 49 - 52, 08.03.2010

Abstract

References

  • Aubin, J-P., Ekeland, I., “Applied Nonlinear Analysis”, Wiley-İnterscience, New York, USA, 159-200 (1984).
  • Azimov, A. Y., Gasimov R. N., “On weak conjugacy, weak subdifferentials and duality with zero International Journal of Applied Mathematics, 1:171-192 (1999). optimization”,
  • Azimov, A. Y., Gasimov R. N., “Stability and duality of nonconvex problems via augmented lagrangian”, Cybenetics and Systems Analysis, 38:412-421 (2002).
  • Clarke F.H., “A new approach to lagrange multipliers”, Mathematics Operations Research, 1:165-174 (1976).
  • Clarke F.H., “Optimization and Nonsmooth Analysis”, Wiley-İnterscience, New York, USA, 9-30 (1983).
  • Ekeland I., Temam R., “Convex Analysis and Variational Problems”, Elsevier Norht-Holland, Amsterdam, 3-34 (1983).
  • Rocafellar R. T., “Convex Analysis”, Princeton University, New Jersey, USA, 215-227 (1970).
  • Kasımbeyli R. N., “Radial Epiderivatives and Set Valued Optimization”, Optimization, 58(5):521- 534 (2009).
  • Rocafellar R. T., “Proximal subgradients, marginal values and augmented lagrangian in nonconvex optimization”, Math. Oper. Res., 6:427-437, (1981).
  • Rocafellar R. T., “Lagrange multipliers and optimality”, SIAM Review, 35:183-238 (1993).
There are 10 citations in total.

Details

Primary Language English
Journal Section Industrial Engineering
Authors

Refail Kasımbeylı This is me

Gonca İnceoğlu

Publication Date March 8, 2010
Published in Issue Year 2010 Volume: 23 Issue: 1

Cite

APA Kasımbeylı, R., & İnceoğlu, G. (2010). The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science, 23(1), 49-52.
AMA Kasımbeylı R, İnceoğlu G. The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science. March 2010;23(1):49-52.
Chicago Kasımbeylı, Refail, and Gonca İnceoğlu. “ ”. Gazi University Journal of Science 23, no. 1 (March 2010): 49-52.
EndNote Kasımbeylı R, İnceoğlu G (March 1, 2010) The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science 23 1 49–52.
IEEE R. Kasımbeylı and G. İnceoğlu, “ ”., Gazi University Journal of Science, vol. 23, no. 1, pp. 49–52, 2010.
ISNAD Kasımbeylı, Refail - İnceoğlu, Gonca. “ ”. Gazi University Journal of Science 23/1 (March 2010), 49-52.
JAMA Kasımbeylı R, İnceoğlu G. The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science. 2010;23:49–52.
MLA Kasımbeylı, Refail and Gonca İnceoğlu. “ ”. Gazi University Journal of Science, vol. 23, no. 1, 2010, pp. 49-52.
Vancouver Kasımbeylı R, İnceoğlu G. The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science. 2010;23(1):49-52.