Reducing the number of AD passes for computing a sparse Jacobian matrix

A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution … Read more

Constraint Identification and Algorithm Stabilization for Degenerate Nonlinear Programs

In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so … Read more

iNEOS : An Interactive Environment for Nonlinear Optimization

In this paper we describe iNEOS, an Internet-based environment which facilitates the solution of complex nonlinear optimization problems. It enables a user to easily invoke a remote optimization code without having to supply the model to be optimized. An interactive communication between client and server is established and maintainted using CORBA. We test the system … Read more

Benchmarking Optimization Software with COPS

We describe version 2.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the LANCELOT, LOQO, MINOS, and SNOPT solvers on these problems. Citation Technical Report ANL/MCS-246 Mathematics and Computer Science Division Argonne National … Read more

Feasibility Control in Nonlinear Optimization

We analyze the properties that optimization algorithms must possess in order to prevent convergence to non-stationary points for the merit function. We show that demanding the exact satisfaction of constraint linearizations results in difficulties in a wide range of optimization algorithms. Feasibility control is a mechanism that prevents convergence to spurious solutions by ensuring that … Read more

An infeasible active set method for convex problems with simple bounds

A primal-dual active set method for convex quadratic problems with bound constraints is presented. Based on a guess on the active set, a primal-dual pair $(x,s)$ is computed that satisfies the first order optimality condition and the complementarity condition. If $(x,s)$ is not feasible, a new active set is determined, and the process is iterated. … Read more

On the global convergence of an SLP-filter algorithm

A mechanism for proving global convergence infilter-type methods for nonlinear programming is described. Such methods are characterized by their use of the dominance concept of multi objective optimization, instead of a penalty parameter whose adjustment can be problematic. The main point of interest is to demonstrate how convergence for NLP can be induced without forcing … Read more

On reduced QP formulations of monotone LCP problems

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation—one that has fewer constraints than the “standard” QP formulation—is available. We mention several instances of this class, including the known case in which the … Read more

Failure of Global Convergence for a Class of Interior Point Methods for Nonlinear Programming

Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms do produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed … Read more