ISSN:
1573-2878
Keywords:
Constrained optimization
;
equality constrained problems
;
penalty parameters
;
nonmonotonic penalty parameters
;
convergence
;
trust-region methods
;
first-order point
;
second-order point
;
necessary conditions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In a recent paper (Ref. 1), the author proposed a trust-region algorithm for solving the problem of minimizing a nonlinear function subject to a set of equality constraints. The main feature of the algorithm is that the penalty parameter in the merit function can be decreased whenever it is warranted. He studied the behavior of the penalty parameter and proved several global and local convergence results. One of these results is that there exists a subsequence of the iterates generated by the algorithm that converges to a point that satisfies the first-order necessary conditions. In the current paper, we show that, for this algorithm, there exists a subsequence of iterates that converges to a point that satisfies both the first-order and the second-order necessary conditions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192282
Permalink