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Avoiding the Maratos effect by means of a nonmonotone line search. I: General constrained problems. (English) Zbl 0732.65055

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.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C20 Quadratic programming

Citations:

Zbl 0616.65067
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