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

Authors:
Choong Ming Chin;Abdul Halim Abdul Rashid;Khalid Mohamed Nor
Affiliations:
Asian Research Centre, Cyberjaya, Selangor, Malaysia;Mathematical Sciences Institute, University of Malaya, Kuala Lumpur, Malaysia;Department of Electrical Engineering, Technological University of Malaysia, Skudai, Johor, Malaysia
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

A framework for proving global convergence for a class of line search filter-type methods for nonlinear programming is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the filter concept where trial points are accepted, provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve a sequence of quadratic programming subproblems via line search techniques to induce global convergence. Under mild conditions, we will also show that the algorithm converges two step superlinearly when the iterates are near to the solution.