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A sequential quadratic programming algorithm with non-monotone line search
Dai, Yu-Hong1; Schittkowski, Klaus2
AbstractToday, many practical smooth nonlinear programming problems are routinely 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 assuming 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 a drastic improvement of the performance is achieved compared to monotone line search. This situation is very typical for complex simulation programs producing inaccurate function values and where, even worse, derivatives are nevertheless computed by forward differences.
KeywordSQP sequential quadratic programming nonlinear programming non-monotone line search merit function convergence numerical results
Funding ProjectAlexander von Humboldt foundation[CHN/1112740 STP]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000258567800010
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Document Type期刊论文
Corresponding AuthorDai, Yu-Hong
Affiliation1.Chinese Acad Sci, State Key Lab Sci & Eng Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Bayreuth, Dept Comp Sci, D-95440 Bayreuth, Germany
Recommended Citation
GB/T 7714
Dai, Yu-Hong,Schittkowski, Klaus. A sequential quadratic programming algorithm with non-monotone line search[J]. PACIFIC JOURNAL OF OPTIMIZATION,2008,4(2):335-351.
APA Dai, Yu-Hong,&Schittkowski, Klaus.(2008).A sequential quadratic programming algorithm with non-monotone line search.PACIFIC JOURNAL OF OPTIMIZATION,4(2),335-351.
MLA Dai, Yu-Hong,et al."A sequential quadratic programming algorithm with non-monotone line search".PACIFIC JOURNAL OF OPTIMIZATION 4.2(2008):335-351.
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