Abstract
A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second‐order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.
Highlights
Fletcher and Leyffer 1 proposed filter methods in 2002 offering an alternative to traditional merit functions in solving nonlinear programming problems NLPs
Filter methods avoid the difficulty of determining a suitable value of the penalty parameter in the merit function
Two variants of trustregion filter sequential quadratic programming SQP method were proposed by Fletcher et al 2, 3
Summary
Fletcher and Leyffer 1 proposed filter methods in 2002 offering an alternative to traditional merit functions in solving nonlinear programming problems NLPs. Wachter and Biegler 9, proposed a line-search filter method and applied it to different algorithm framework. It has been noted by Fletcher and Leyffer 1 that the filter approach can suffer from the Maratos effect as that of a penalty function approach. By the Maratos effect, a full step can lead to an increase of both infeasibility measure and objective function in filter components even if arbitrarily close to a regular minimizer. This makes the full step unacceptable for the filter and can prohibit fast local convergence. We propose a filter algorithm with inexact line-search for nonlinear programming problems that ensures superlinear local convergence without second-order correction steps.
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