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