## Implementation of a Sequential Quadratic Programming Algorithm for Parallel
Computing

K. Schittkowski, Report, Department of Mathematics, University of Bayreuth (2002)

**Abstract:** The paper introduces a new version of the SQP code
NLPQL, which is widely used in commercial and academic
institutions to solve smooth nonlinear programming problems. The new version, NLPQLP, is specifically tuned to run under
distributed systems. Another input parameter L is introduced for the number of parallel machines, that is the number of
function calls to be executed simultaneously. In case of L=1, NLPQLP is identical to
NLPQL. Otherwise the line search procedure is modified to allow parallel function calls, which can also be applied for approximating gradients by difference
formulae. The mathematical background is outlined, in particular the modification of the line search algorithm to retain
convergence under parallel systems. Numerical results show the sensitivity of the new version with respect to the number of
parallel machines and the influence of different gradient approximations under uncertainty. The performance evaluation is
obtained by more than 300 standard test problems. It must be emphasized that the distributed computation of function values is
only simulated throughout the paper. It is up to the user to adopt the code to a particular parallel environment.

To download a preprint, click here: NLPQLP_perf.pdf