On the use of piecewise linear models in nonlinear programming

This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linear-quadratic programming (SL-QP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian.