In this paper, a new weighted short-step primal-dual interior point algorithm for convex quadratic optimization (CQO) problems is presented. The algorithm uses at each interior point iteration only full-Newton steps and the strategy of the central path to obtain an ε-approximate solution of CQO. This algorithm yields the best currently wellknown theoretical iteration bound, namely, O( √ n log ε...

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are co...

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. New regularization techniques for Newton systems applicable to both symmetric positive de nite and symmetric inde nite systems are described. They transform the latter to quaside nite systems known to be strongly ...

23] C.L. Monma and A.J. Morton. Computational experimental with a dual aane variant of Karmarkar's method for linear programming. extension of Karmarkar type algorithm to a class of convex separable programming problems with global linear rate of convergence. Techni-28] J. Renegar. A polynomial-time algorithm based on Newton's method for linear programming. Implementing an interior point method...

Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or the...

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are co...

The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points with a good generalization performance. In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses the analytic center cutting plane method restricted to spherical shells. In this work we prove existence a...

In the adaptive step primal dual interior point method for linear programming polynomial algorithms are obtained by computing Newton directions towards targets on the central path and restricting the iterates to a neighborhood of this central path In this paper the adaptive step methodology is extended by considering targets in a certain central region which contains the usual central path and ...

One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal-dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set of linear and mixed integer ...

The literature in the eld of interior point methods for linear programming has been almost exclusively algorithm oriented. Recently G uler, Roos, Terlaky and Vial presented a complete duality theory for linear programming based on the interior point approach. In this paper we present a more simple approach which is based on an embedding of the primal problem and its dual into a skew symmetric ...