Limiting Behavior and Analyticity of Two Special Types of Infeasible Weighted Central Paths in Semidefinite Programming

نویسنده

  • M. TRNOVSKÁ
چکیده

The central path is the most important concept in the theory of interior point methods. It is an analytic curve in the interior of the feasible set which tends to an optimal point at the boundary. The analyticity properties of the paths are connected with the analysis of the superlinear convergence of the interior point algorithms for semidefinite programming. In this paper we study the analyticity of two special types of weighted central paths in semidefinite programming, under the condition of the existence of the strictly complementary solution.

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

Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming

This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form XS + SX = 2νW , where W is a fixed positive definite matrix and ν > 0 is a parameter, under the assumption that the problem has a strictly complementary primal–dual optimal solution. We present a different and simpler proof than the one given ...

متن کامل

Error Bounds and Limiting Behavior of Weighted Paths Associated with the SDP Map X1/2SX1/2

This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming (SDP) obtained from centrality equations of the form X1/2SX1/2 = νW , where W is a fixed positive definite matrix and ν > 0 is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution. It is shown that a weighted central path as a functio...

متن کامل

A path-following infeasible interior-point algorithm for semidefinite programming

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

متن کامل

Analyticity of weighted central paths and error bounds for semidefinite programming

The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semidefinite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of strictly complementary solutions. Secondl...

متن کامل

Analysis of Interior-Point Paths

Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning ...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010