readcube_id
ae36da270864ee00636fd19f327807f44f56eb9f92c21ecd0cd723eb652b8988
Powell
M. J. D.
en
research_article
http://link.springer.com/10.1007%2FBF01589118
false
1989-08-01
547-566
1989-08
2019-04-10T15:56
A tolerant algorithm for linearly constrained optimization calculations
Two extreme techniques when choosing a search direction in a linearly constrained optimization calculation are to take account of all the constraints or to use an active set method that satisfies selected constraints as equations, the remaining constraints being ignored. We prefer an intermediate method that treats all inequality constraints with “small” residuals as inequalities with zero right hand sides and that disregards the other inequality conditions. Thus the step along the search direction is not restricted by any constraints with small residuals, which can help efficiency greatly, particularly when some constraints are nearly degenerate. We study the implementation, convergence properties and performance of an algorithm that employs this idea. The implementation considerations include the choice and automatic adjustment of the tolerance that defines the “small” residuals, the calculation of the search directions, and the updating of second derivative approximations. The main convergence theorem imposes no conditions on the constraints except for boundedness of the feasible region. The numerical results indicate that a Fortran implementation of our algorithm is much more reliable than the software that was tested by Hock and Schittkowski (1981). Therefore the algorithm seems to be very suitable for general use, and it is particularly appropriate for semi-infinite programming calculations that have many linear constraints that come from discretizations of continua.
https://scigraph.springernature.com/explorer/license/
articles
10.1007/bf01589118
doi
1-3
dimensions_id
pub.1036571828
Numerical and Computational Mathematics
University of Cambridge
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, England
Springer Nature - SN SciGraph project
Mathematical Sciences
1436-4646
0025-5610
Mathematical Programming
45