Abstract :
Since their introduction in 1969, independently, by Hestenes [10] and Powell [13], multiplier methods have become a very popular tool for constrained optimization. At present, we find a sizeable literature dealing with the two main forms of these methods: those of the sequential unconstrained minimization type, which was originally proposed by Hestenes [10] and Powell [13] and those of the continuous multiplier update type first proposed by Fletcher [5]. An excellent review of the literature on sequential minimization type methods can be found in the survey papers by Rockafellar [20], Fletcher [6], Bertsekas [1] and Powell [14] as well as in the book by Pierre and Lowe [15]. A number of major results on continuous multiplier update type methods can be found in the work of Fletcher and his collaborators [7,8] and of Mukai and Polak [12] and Glad and Polak [9]. For the sequential minimization type methods, we find results on local convergence, rate of convergence, with both increasing and finite penalty, and the effects of approximate unconstrained minimization [2,3, 4,17,19], but no theoretical results on automatic penalty limitation. For continuous multiplier update methods we find results on global convergence, rate of convergence and automatic penalty limitation [12,9].
