A. Schwartz et E. Polak, FAMILY OF PROJECTED DESCENT METHODS FOR OPTIMIZATION PROBLEMS WITH SIMPLE BOUNDS, Journal of optimization theory and applications, 92(1), 1997, pp. 1-31
Citations number
27
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
This paper presents a family of projected descent direction algorithms
with inexact line search for solving large-scale minimization problem
s subject to simple bounds on the decision variables. The global conve
rgence of algorithms in this family is ensured by conditions on the de
scent directions and line search. Whenever a sequence constructed by a
n algorithm in this family enters a sufficiently small neighborhood of
a local minimizer (x) over cap satisfying standard second-order suffi
ciency conditions, it gets trapped and converges to this local minimiz
er. Furthermore, in this case, the active constraint set at (x) over c
ap is identified in a finite number of iterations. This fact is used t
o ensure that the rate of convergence to a local minimizer, satisfying
standard second-order sufficiency conditions, depends only on the beh
avior of the algorithm in the unconstrained subspace. As a particular
example, we present projected versions of the modified Polak-Ribiere c
onjugate gradient method and the limited-memory BFGS quasi-Newton meth
od that retain the convergence properties associated with those algori
thms applied to unconstrained problems.