A Sequential Quadratic Programming Algorithm with Non-Monotone Line Search Yu-Hong Dai State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science, Chinese Academy of Sciences P. O. Box 2719, Beijing 100080, P. R. China Email: dyh@lsec.cc.ac.cn Klaus Schittkowski Department of Computer Science, University of Bayreuth D - 95440 Bayreuth, Germany. Email: klaus.schittkowski@uni-bayreuth.de Abstract Today, many practical smooth nonlinear programming problems are rou- tinely solved by sequential quadratic programming (SQP) methods stabilized by a monotone line search procedure subject to a suitable merit function. In case of computational errors as for example caused by inaccurate function or gradient evaluations, however, the approach is unstable and often terminates with an error message. To reduce the number of false terminations, a non- monotone line search is proposed which allows the acceptance of a step length even with an increased merit function value. Thus, the subsequent step may become larger than in case of a monotone line search and the whole iteration process is stabilized. Convergence of the new SQP algorithm is proved as- suming exact arithmetic, and numerical results are included. As expected, no significant improvements are observed if function values are computed within machine accuracy. To model more realistic and more difficult situations, we add randomly generated errors to function values and show that despite of in- creased noise a drastic improvement of the performance is achieved compared to monotone line search. This situation is very typical for complex simula- tion programs producing inaccurate function values and where, even worse, derivatives are nevertheless computed by forward differences. Keywords : SQP, sequential quadratic programming, nonlinear programming, non- monotone line search, merit function, convergence, numerical results 1