Panier, Eliane R.; Tits, André L. Avoiding the Maratos effect by means of a nonmonotone line search. I: General constrained problems. (English) Zbl 0732.65055 SIAM J. Numer. Anal. 28, No. 4, 1183-1195 (1991). The authors present a new line search for sequential quadratic programming algorithms that intend to solve nonlinear programming problems. This nonmonotone line search accepts the step 1 if a sufficient decrease is obtained compared to the last four values of the exact penalty function. This avoids any restauration and extends to constrained optimization a technique due to L. Grippo, F. Lampariello and S. Lucidi [ibid. 23, 707-716 (1986; Zbl 0616.65067)]. In a companion paper (part II, to appear in SIAM J. Numer. Anal.) it will be shown how to use this idea in order to obtain feasible iterates. Reviewer: J.F.Bonnans (Le Chesnay) Cited in 2 ReviewsCited in 59 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C20 Quadratic programming Keywords:Maratos effect; backtracking; sequential quadratic programming algorithms; nonlinear programming problems; nonmonotone line search; penalty function Citations:Zbl 0616.65067 PDFBibTeX XMLCite \textit{E. R. Panier} and \textit{A. L. Tits}, SIAM J. Numer. Anal. 28, No. 4, 1183--1195 (1991; Zbl 0732.65055) Full Text: DOI