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A penalty-free-type two-step linear search algorithm. (Chinese. English summary) Zbl 1212.90361
Summary: Inspired by the work of M. Ulbrich and S. Ulbrich [Math. Program. 95, No. 1 (B), 103–135 (2003; Zbl 1030.90123)], a two-step linear search algorithm is presented in which a tangential direction and a normal direction are computed for each time, and the step-length is determined through a backtracing search. To ensure the global convergence, it is required that there must be a certain relationship to be satisfied between the reductions in normal and tangential directions and the reduction of the function. In the algorithm, no penalty function is needed, and the amount for the computation of the search direction is much smaller. For testing the effectiveness of the algorithm, some numerical experiments are carried out.
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods