ISSN:
1573-2878
Schlagwort(e):
Nonlinear programming
;
linear constraints
;
algorithms
;
global convergence
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In this paper, an algorithm is developed for solving a nonlinear programming problem with linear contraints. The algorithm performs two major computations. First, the search vector is determined by projecting the negative gradient of the objective function on a polyhedral set defined in terms of the gradients of the equality constraints and the near binding inequality constraints. This least-distance program is solved by Lemke's complementary pivoting algorithm after eliminating the equality constraints using Cholesky's factorization. The second major calculation determines a stepsize by first computing an estimate based on quadratic approximation of the function and then finalizing the stepsize using Armijo's inexact line search. It is shown that any accumulation point of the algorithm is a Kuhn-Tucker point. Furthermore, it is shown that, if an accumulation point satisfies the second-order sufficiency optimality conditions, then the whole sequence of iterates converges to that point. Computational testing of the algorithm is presented.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00933968
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