id: 04092674
dt: j
an: 04092674
au: Gould, Nicholas Ian Mark
ti: On the convergence of a sequential penalty function method for constrained
    minimization.
so: SIAM J. Numer. Anal. 26, No.1, 107-128 (1989).
py: 1989
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: sequential penalty function method; constrained optimization; Q-
    superlinear convergence; Q-linear convergence; algorithms; equality
    constraints; augmented Lagrangians; quadratic penalty functions
ci: 
li: doi:10.1137/0726007
ab: This interesting paper analyzes the convergence of a class of algorithms
    for minimizing f(x) subject to equality constraints $c\sb i(x)=0$,
    derived from a penalty function of type $f+\sum u\sb kc\sb k+\sum c\sp
    2\sb k/2μ$ which is minimized for a sequence of $μ$-values
    $μ\sp{(i)}\to 0$. Important special instances are augmented
    Lagrangians and quadratic penalty functions. One of the results is,
    that under mild conditions on the problem, $μ$-sequences are
    characterized such that the iterates $x\sp{(i)}$ converge two-step
    Q-linearly (Q-superlinearly), if the $μ$-sequence converges Q-linearly
    (Q-superlinearly). A step in this context means evaluation of f, $c\sb
    i$ and (first and second order) derivatives.
rv: R.Hettich