In this paper we study some basic properties of the Moreau-Yosida function with two variables , and generalize the results of related to study of the convergence for sequence of convex-concave functions and the sequence of Moreau-Yosida function corr
esponding , and the basic theorem that we proved is : for any sequence of convex-concave functions , if they are convergent of the Moreau-Yosida distance then the sequence of Moreau-Yosida function corresponding will be convergent to the concept of Mosco-epi/hypo graph convergence .
we constructed a continuation predictor- corrector algorithm that
solves constrained optimization problems. Smooth penalty functions combined
with numerical continuation, along with the use of the expanded Lagrangian
system, were essential compone
nts of the algorithm. An improvement of this
algorithm was published, which dealt with the linear algebra in the
corrector part of the algorithm.
