The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.

1. Abstract Complementarity problems arise in mathematical models of several applications in Engineering, Economy and different branches of Physics. We mention contact problems and dynamic of multiple body systems in Solid Mechanics. In this paper we present a new feasible directions interior-point algorithm for mixed nonlinear complementarity problems that we have called FDA-MNCP. This algorit...

We present an extension, for nonlinear optimization under linear constraints, of an algorithm for quadratic programming using a trust region idea introduced by Ye and Tse [Math. Programming, 44 (1989), pp. 157–179] and extended by Bonnans and Bouhtou [RAIRO Rech. Opér., 29 (1995), pp. 195–217]. Due to the nonlinearity of the cost, we use a linesearch in order to reduce the step if necessary. We...

Despite the efficiency shown by interior-point methods in large-scale linear programming, they usually perform poorly when applied to multicommodity flow problems. The new specialized interior-point algorithm presented here overcomes this drawback. This specialization uses both a preconditioned conjugate gradient solver and a sparse Cholesky factorization to solve a linear system of equations a...

In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obt...

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

Mathematical program with equilibrium constraints (MPEC) has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC. A primal-dual interior point method is then proposed, which solves a sequence of relaxe...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...