Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more
This paper describes numerical experience with solving MPECs as NLPs on a large collection of test problems. The key idea is to use off-the-shelf NLP solvers to tackle large instances of MPECs. It is shown that SQP methods are very well suited to solving MPECs and at present outperform Interior Point solvers both in terms … Read more
An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration, and perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQP approaches: … Read more
Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience … Read more
Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs). In particular, Sequential Quadratic Programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. It is shown that SQP converges superlinearly under reasonable assumptions … Read more
The Fortran subroutine NLPQLP solves smooth nonlinear programming problems and is an extension of the code NLPQL. The new version is specifically tuned to run under distributed systems. A new input parameter l is introduced for the number of parallel machines, that is the number of function calls to be executed simultaneously. In case of … Read more
An algorithm for solving equality constrained optimization problems is proposed. It can deal with nonconvex functions and uses a truncated conjugate algorithm for detecting nonconvexity. The algorithm ensures convergence from remote starting point by using line-search. Numerical experiments are reported, comparing the approach with the one implemented in the trust region codes ETR and Knitro. … Read more
Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior … Read more
A series of numerical experiments with interior point (LOQO, KNITRO) and active-set SQP codes (SNOPT, filterSQP) are reported and analyzed. The tests were performed with small, medium-size and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and several suggestions on how to improve them are presented. … Read more
A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more