A reduced Hessian algorithm with line search filter method for nonlinear programming
The authors consider the problem of minimizing a nonlinear function subject to a set of nonlinear equality constraints, where the objective function and the equality constraints are sufficiently smooth. Filter algorithms (introduced by \textit{R. Fletcher, S. Leyffer} and \textit{P. L. Toint} [SIAM J. Optim. 13, No.~1, 44--59 (2002; Zbl 1029.65063)]) use a function that aggregates constraint violations and then treats the resulting biobjective problem. A step is accepted if it reduces the value either of the objective function or of the constraint violation. This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, and second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. A numerical experiment is reported to show the effectiveness of the proposed algorithm.
scientific article; zbMATH DE number 5907616
scientific article