A Filter Inexact-Restoration Method for Nonlinear Programming Cândida Elisa P. Silva * M. Teresa T. Monteiro † January 5, 2009 Abstract A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear con- strained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. [7] but not yet implemented - the internal algorithms are not proposed. The filter, a new concept intro- duced by Fletcher and Leyffer [3], replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration - the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided. Keywords: Filter Method, Inexact-Restoration, Line Search. 1 Introduction The inexact-restoration method introduced by Martínez [9] and also used in [8] treats feasibility and optimality as two independent phases. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved (a “more feasible” point is computed with respect * Management and Industrial School, Polytechnic Institute of Porto, Portugal candidasilva@eseig.ipp.pt † University of Minho, Portugal tm@dps.uminho.pt 1