Extended Lagrange and penalty functions in optimization

Journal of Optimization Theory and Applications

Volumn 111, Issue 2, 2001, Pages 381-405

  Rubinov, A M ^a   Yang, X Q ^b   Glover, B M ^c  

^a UNIVERSITY OF BALLARAT   (Australia)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

Exact penalization; Increasing positively homogeneous functions; Lagrange multipliers; Penalty coefficients; Regular weak separation functions; Zero duality gap

Indexed keywords

EXACT PENALIZATION; HOMOGENEOUS FUNCTIONS; INCREASING POSITIVELY HOMOGENEOUS FUNCTION; LAGRANGE FUNCTIONS; OPTIMISATIONS; PENALTY COEFFICIENT; PENALTY FUNCTION; REGULAR WEAK SEPARATION FUNCTION; SEPARATION FUNCTIONS; ZERO DUALITY GAPS;

LAGRANGE MULTIPLIERS;

EID: 0040780610     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1011938519299     Document Type: Article

References (14)

1. YEVTUSHENKO, Yu. G., and ZHADAN, V. G., Auxiliary Functions in Optimization Problems, USSR Journal of Computational Mathematics and Mathematical Physics, Vol. 30, pp. 31-42, 1990.
2. ZABOTIN, YA. I., A Minimax Method for Solving Problems of Mathematical Programming, Soviet Mathematics, Vol. 19, pp. 28-33, 1975.
3. GROSSMAN, C., and KAPLAN, A., Straffunktionen und Modifizierte Lagrange-funktionen in der Nichtlinearen Optimierund, Teubner Texte zur Mathematik, Leipzig, Germany, 1979.
4. GOH, C. J., and YANG, X. Q., A Nonlinear Lagrangian Theory for Nonconvex Optimization Problems, Journal of Optimization Theory and Applications, Vol. 109, pp. 99-121, 2001.
5. GOH, C. J., and YANG, X. Q., A Sufficient and Necessary Condition for Nonconvex Constrained Optimization, Applied Mathematics Letters, Vol. 10, pp. 9-12, 1997.
6. Li, D., Zero Duality Gap for a Class of Nonconvex Optimization Problems, Journal of Optimization Theory and Applications, Vol. 85, pp. 309-324, 1995.
7. RUBINOV, A. M., GLOVER, B. M., and YANG, X. Q., Extended Lagrange and Penalty Functions in Continuous Optimization, Optimization, Vol. 46, pp. 326-351, 1999.
8. RUBINOV, A. M., GLOVER, B., and YANG, X. Q., Decreasing Functions with Applications to Penalization, SIAM Journal on Optimization, Vol. 10, pp. 289-313, 1999.
9. ANDRAMONOV, M. Yu., An Approach to Constructing Generalized Penalty Functions, Optimization and Related Topics, Edited by A. M. Rubinov and B. M. Glover, Kluwer Academic Publishers, Dordrecht, Holland, pp. 3-14, 2001.
10. GIANNESSI, F., Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331-365, 1984.
11. RUBINOV, A. M., and UDERZO, A., On Global Optimality Conditions via Separation Functions, Journal of Optimization Theory and Applications (to appear).
12. RUBINOV, A. M., and GLOVER, B. M., Duality for Increasing Positively Homogeneous Functions and Normal Sets, RAIRO Operations Research, Vol. 32, pp. 105-123, 1997.
13. BURKE, J. V., An Exact Penalization Viewpoint of Constrained Optimization, SIAM Journal of Control and Optimization, Vol. 29, pp. 968-998, 1991.
14. ROCKAFELLAR, R. T., Conjugate Duality and Optimization, CBMS Lecture Note Series, SIAM Publications, Philadelphia, Pennsylvania, Vol. 162, 1974.