Global and local convergence of a filter line search method for nonlinear programming

A new non-monotone filter trust region algorithm for solving nonlinear systems of equalities and inequalities

“…In order to overcome the Maratos effect, we modify the non-monotone filter trust region algorithm by introducing second order correction step, which is denoted by s soc k . Similar to Chin, Rashid and Nor [2], we calculate the second order correction step s soc k by solving a modified QP subproblem…”

“…Filter methods were presented by Fletcher and Leyffer [6] for nonlinear programming, offering an alternative to merit functions, as a tool to guarantee global convergence of algorithms for nonlinear optimization. Filter methods were successfully applied to solve various optimization problems [2,6,7,8,9,10,11,13,21,23,24,25,29].…”

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

“…As usual, the inequalities in ap(c, x k , d) ≤ 0 are understood component-wise. Clearly, one can select any reasonable method for solving (9), but in practice different variants (see, e.g., Fletcher et al, 2002a;2002b;Chin, 2007) of Quadratic Programming (QP) are used when ap(f,…”

“…In a series of papers (Chin and Fletcher, 2003;Chin, 2007;Fletcher and Leyffer, 2002;Fletcher et al, 2002a;2002b;Audet and Dennis, 2004;Fletcher, 2010;Ulbrich, 2004;Su and Yu, 2009), Fletcher and coworkers developed a filter approach to nonlinear programming problems. This approach is a breakthrough in constructing optimization solvers, because it clearly puts an emphasis on the fact that coping with nonlinear constraints is as difficult and as important as finding the minimum of an objective function.…”

Line search SQP method with a flexible step acceptance procedure

“…Subsequently, global convergence of the trust-region filter SQP method was established by Fletcher et al [9,12]. Extension of optimization techniques using filter strategy can be found in line search methods [7,29], interior point approaches [2,28], bundle methods for non-smooth optimization [10,20] and derivative-free optimization approaches [1]. More theoretical and algorithmic details on filter methods can be seen, for example, in [6,16,26,27].…”