BibTex RIS Kaynak Göster

The Properties of The Weak Subdifferentials. . .

Yıl 2010, Cilt: 23 Sayı: 1, 49 - 52, 08.03.2010

Öz

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.

 

Kaynakça

  • 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).
Yıl 2010, Cilt: 23 Sayı: 1, 49 - 52, 08.03.2010

Öz

Kaynakça

  • 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).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Industrial Engineering
Yazarlar

Refail Kasımbeylı Bu kişi benim

Gonca İnceoğlu

Yayımlanma Tarihi 8 Mart 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 23 Sayı: 1

Kaynak Göster

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. Mart 2010;23(1):49-52.
Chicago Kasımbeylı, Refail, ve Gonca İnceoğlu. “ ”. Gazi University Journal of Science 23, sy. 1 (Mart 2010): 49-52.
EndNote Kasımbeylı R, İnceoğlu G (01 Mart 2010) The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science 23 1 49–52.
IEEE R. Kasımbeylı ve G. İnceoğlu, “ ”., Gazi University Journal of Science, c. 23, sy. 1, ss. 49–52, 2010.
ISNAD Kasımbeylı, Refail - İnceoğlu, Gonca. “ ”. Gazi University Journal of Science 23/1 (Mart 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 ve Gonca İnceoğlu. “ ”. Gazi University Journal of Science, c. 23, sy. 1, 2010, ss. 49-52.
Vancouver Kasımbeylı R, İnceoğlu G. The Properties of The Weak Subdifferentials. . . Gazi University Journal of Science. 2010;23(1):49-52.