Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

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

Interior-Point Methods for Nonconvex Nonlinear Programming: Complementarity Constraints

In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interior-point method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the … Read more

A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties.

An exact-penalty-function-based scheme—inspired from an old idea due to Mayne and Polak (Math. Prog., vol.~11, 1976, pp.~67–80)—is proposed for extending to general smooth constrained optimization problems any given feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior-point framework allows for a simpler penalty parameter update rule than that discussed and … Read more

A new exact penalty function

For constrained smooth or nonsmooth optimization problems, new continuously differentiable penalty functions are derived. They are proved exact in the sense that under some nondegeneracy assumption, local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function. This is achieved by augmenting the dimension of the program by a variable that … Read more

Combinatorial Structures in Nonlinear Programming

Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible … Read more

The Penalty Interior Point Method fails to converge for Mathematical Programs with Equilibrium Constraints

This paper presents a small example for which the Penalty Interior Point Method converges to a non-stationary point. The reasons for this adverse behaviour are discussed. Citation Numerical Analysis Report NA/208, Department of Mathematics, University of Dundee, February 2002. Article Download View The Penalty Interior Point Method fails to converge for Mathematical Programs with Equilibrium … Read more

Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints

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

Relations between divergence of multipliers and convergence to infeasible points in primal-dual interior methods for nonconvex nonlinear programming

Recently, infeasibility issues in interior methods for nonconvex nonlinear programming have been studied. In particular, it has been shown how many line-search interior methods may converge to an infeasible point which is on the boundary of the feasible region with respect to the inequality constraints. The convergence is such that the search direction does not … Read more

A New Mathematical-Programming Framework for Facility-Layout Design

We present a new framework for efficiently finding competitive solutions for the facility-layout problem. This framework is based on the combination of two new mathematical-programming models. The first model is a relaxation of the layout problem and is intended to find good starting points for the iterative algorithm used to solve the second model. The … Read more

A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs

We present a primal-dual interior-point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior-point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter rho in the merit function is updated automatically such … Read more