In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl 1 QP.

Abstract. This paper gives an extensive documentation of applications of finite-dimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.

Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs).

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 of speed and reliability. All NLP solvers also compare very favourably to special MPEC solvers on tests published in the literature.

A modified Cholesky factorization algorithm introduced originally by Gill and Murray and refined by Gill, Murray and Wright, is used extensively in optimization algorithms. Since its introduction in 1990, a di#erent modified Cholesky factorization of Schnabel and Eskow has also gained widespread usage. Compared with the Gill-Murray-Wright algorithm, the Schnabel-Eskow algorithm has a smaller a priori bound on the perturbation added to ensure positive definiteness, and some computational advantages, especially for large problems. Users of the Schnabel-Eskow algorithm, however, have reported cases from two di#erent contexts where it makes a far larger modification to the original matrix than is necessary and than is made by the Gill-Murray-Wright method. This paper reports a simple modification to the Schnabel-Eskow algorithm that appears to correct all the known computational di#culties with the method, without harming its theoretical properties, or its computational behavior in any ot...

this paper, we will concentrate on the overspeci#cation arising from the ASCs and will not consider other possible errors sources.

Abstract. In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter ” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl1QP. Key words. nonlinear programming – SQP – filter – penalty function