A nonmonotone inexact filter SQP algorithm

We present a nonmonotone inexact filter sequential quadratic programming algorithm for solving general nonlinear programs. In each step of this algorithm, to find a search direction, a linear program is first solved to reduce the constraint violation and obtain the steering direction.Using the solution of this linear program, a feasible convex quadratic programming approximation is defined for the nonlinear problem. Instead of solving this subproblem exactly, we invoke a QP solver to find an inexact solution satisfying some loose and achievable conditions. This inexact solution is used as the search direction. The search direction is a descent direction for the constraint violation and/or the objective function. Moreover, it is a descent direction for the penalty function using an appropriate penalty parameter updating rule. To prevent an occurrence of the Maratos phenomenon, we use a nonmonotone line search procedure based on a filter technique. We implementthis algorithm using FORTRAN. The preliminary numerical experiment on some test problem shows the efficiency and reliability of the proposed algorithm

کلیدواژه ها:

Nonlinear programming ، Sequential quadratic programming ، Inexact methods ، Filter methods ، Nonmonotone algorithms ، Maratos effect