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Adaptive two-point stepsize gradient algorithm. (English) Zbl 0992.65063
Authors’ summary: Combined with the nonmonotone line search, the two-point stepsize gradient method has successfully been applied for large-scale unconstrained optimization. However, the numerical performances of the algorithm heavily depend on \(M\), one of the parameters in the nonmonotone line search, even for ill-conditioned problems. This paper proposes an adaptive nonmonotone line search. The two-point stepsize gradient method is shown to be globally convergent with this adaptive nonmonotone line search. Numerical results show that the adaptive nonmonotone line search is specially suitable for the two-point stepsize gradient method.

65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C30 Nonlinear programming
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