An active-set algorithm for nonlinear programming using parametric linear programming

This paper describes an active-set algorithm for nonlinear programming that solves a parametric linear programming subproblem at each iteration to generate an estimate of the active set. A step is then computed by solving an equality constrained quadratic program based on this active-set estimate. This approach respresents an extension of the standard sequential linear-quadratic programming (SLQP) algorithm. It can also be viewed as an attempt to implement a generalization of the gradient projection algorithm for nonlinear programming. To this effect, we explore the relation between the parametric method and the gradient projection method in the bound constrained case. Numerical results compare the performance of this algorithm with SLQP and gradient projection. Department of Computer Science, University of Colorado, Boulder, CO 80309, USA; [email protected]. This author was supported by National Science Foundation grants CCR0219190, CHE-0205170 and CMMI-0728190, and Army Research Office Grant DAAD19-02-1-0407. Department of Industrial & Systems Engineering, University of Southern California, Los Angeles, CA, 90089-0193, USA; [email protected]. This author was supported by National Science Foundation grant CMMI-0728036.