A new approximate proximal point method for minimizing the sum of two conve
x functions is introduced. It replaces the original problem by a sequence o
f regularized subproblems in which the functions are alternately represente
d by linear models. The method updates the linear models and the prox cente
r, as well as the prox coefficient. It is monotone in terms of the objectiv
e values and converges to a solution of the problem, if any. A dual version
of the method is derived and analyzed. Applications of the methods to mult
istage stochastic programming problems are discussed and preliminary numeri
cal experience is presented.