Abstract
It was recently shown that, in the solution of smooth constrained optimization problems by sequential quadratic programming (SQP), the Maratos effect can be prevented by means of a certain nonmonotone (more precisely, three-step or four-step monotone) line search. Using a well-known transformation, this scheme can be readily extended to the case of minimax problems. It turns out however that, due to the structure of these problems, one can use a simpler scheme. Such a scheme is proposed and analyzed in this paper. Numerical experiments indicate a significant advantage of the proposed line search over the Armijo search.
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Communicated by D. Q. Mayne
This research was supported in part by NSF Engineering Research Centers Program No. NSFD-CDR-88-03012, by NSF Grant No. DMC-88-15996, and by a grant from the Westinghouse Corporation.
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Zhou, J.L., Tits, A.L. Nonmonotone line search for minimax problems. J Optim Theory Appl 76, 455–476 (1993). https://doi.org/10.1007/BF00939377
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DOI: https://doi.org/10.1007/BF00939377