Superlinear primal-dual affine scaling algorithms for LCP

نویسندگان

  • Renato D. C. Monteiro
  • Stephen J. Wright
چکیده

We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Superlinear Convergence of Infeasible Interior-Point Algorithms for Linearly Constrained Convex Programs

This note derives bounds on the length of the primal-dual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: 1) the problem has a solution satisfying strict complementarity, 2) the Hessian of the objective function satisfies a certain invariance property. We illustrate the usefulness of these bounds by establishing the superlinea...

متن کامل

Superlinear convergence of the affine scaling algorithm

In this paper we show that a variant of the long-step affine scaling algorithm (with variable stepsizes) is two-step superlinearly convergent when applied to general linear programming (LP) problems. Superlinear convergence of the sequence of dual estimates is also established. For homogeneous LP problems having the origin as the unique optimal solution, we also show that 2 is a sharp upper bou...

متن کامل

Primal Dual Affine Scaling on GPUs

Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimisation problem on GPU based systems. Strategies to convert the system generated by complementary slackness theorem into a symmetric system are given. A new CUDA friendly technique to solve the resulting symmetric positive definite subsystem is also developed. Various strategies to reduce the memory tran...

متن کامل

The primal power affine scaling method

In this paper, we present a variant of the primal affine scaling method, which we call the primal power affine scaling method. This method is defined by choosing a real r > 0.5, and is similar to the power barrier variant of the primal-dual homotopy methods considered by den Hertog, Roos and Terlaky and Sheu and Fang. Here, we analyze the methods for r > 1. The analysis for 0.50 < r < 1 is simi...

متن کامل

A Superlinear Infeasible-Interior-Point Affine Scaling Algorithm for LCP

We present an infeasible-interior-point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence. By choosing the value of a parameter in appropriate ways, polynomial complexity and convergence with Q-order up to (but not including...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Math. Program.

دوره 69  شماره 

صفحات  -

تاریخ انتشار 1995