ISSN:
1573-2878
Keywords:
Nonlinear programming
;
mathematical programming
;
quadratically convergent algorithms
;
conjugate-gradient methods
;
variable-metric methods
;
computing methods
;
numerical methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The problem of minimizing a functionf(x) subject to the constraint ϕ(x)=0 is considered. Here,f is a scalar,x is ann-vector, and ϕ is anm-vector, wherem 〈n. A general quadratically convergent algorithm is presented. The conjugate-gradient algorithm and the variable-metric algorithms for constrained function minimization can be obtained as particular cases of the general algorithm. It is shown that, for a quadratic function subject to a linear constraint, all the particular algorithms behave identically if the one-dimensional search for the stepsize is exact. Specifically, they all produce the same sequence of points and lead to the constrained minimal point in no more thann −r descent steps, wherer is the number of linearly independent constraints. The algorithms are then modified so that they can also be employed for a nonquadratic function subject to a nonlinear constraint. Some particular algorithms are tested through several numerical examples.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933853
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