Augmented Lagrangians which are quadratic in the multiplier

作者: P. T. Boggs , J. W. Tolle

DOI: 10.1007/BF00934785

关键词:

摘要: We present a class of new augmented Lagrangian functions with the essential property that each member is concave quadratic when viewed as function multiplier. This leads to an improved duality theory and related exact penalty functions. In addition, relationship between Newton steps for classical Lagrangians established.

参考文章(9)
M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations Springer Berlin Heidelberg. pp. 144- 157 ,(1978) , 10.1007/BFB0067703
R. A. Tapia, Diagonalized multiplier methods and quasi-Newton methods for constrained optimization Journal of Optimization Theory and Applications. ,vol. 22, pp. 135- 194 ,(1977) , 10.1007/BF00933161
Dimitri P. Bertsekas, COMBINED PRIMAL-DUAL AND PENALTY METHODS FOR CONSTRAINED MINIMIZATION* Siam Journal on Control. ,vol. 13, pp. 521- 544 ,(1975) , 10.1137/0313030
A. Miele, E. E. Cragg, R. R. Iyer, A. V. Levy, Use of the Augmented Penalty Function in Mathematical Programming Problems) Part 1 Journal of Optimization Theory and Applications. ,vol. 8, pp. 115- 130 ,(1971) , 10.1007/BF00928472
Magnus R. Hestenes, Multiplier and gradient methods Journal of Optimization Theory and Applications. ,vol. 4, pp. 303- 320 ,(1969) , 10.1007/BF00927673
Shih-Ping Han, Dual Variable Metric Algorithms for Constrained Optimization SIAM Journal on Control and Optimization. ,vol. 15, pp. 546- 565 ,(1977) , 10.1137/0315037
R.A. Tapia, QUASI-NEWTON METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION: EQUIVALENCE OF EXISTING METHODS AND A NEW IMPLEMENTATION Nonlinear Programming 3#R##N#Proceedings of the Special Interest Group on Mathematical Programming Symposium Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 11–13, 1977. pp. 125- 164 ,(1978) , 10.1016/B978-0-12-468660-1.50010-4