On a general class of interior-point algorithms for semidefinite programming with polynomial complexity and superlinear convergence

On a General Class of Interior-point Algorithms for Semideenite Programming with Polynomial Complexity and Superlinear Convergence

We propose a uniied analysis for a class of infeasible-start predictor-corrector algorithms for semideenite programming problems, using the Monteiro-Zhang uniied direction. The algorithms are direct generalizations of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. We show that the algorithms belonging to this class are globally convergent, provided the problem has a so...

On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems

Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their local and superlinear conver...

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...

Polynomial interior point algorithms for general LCPs

Linear Complementarity Problems (LCP s) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCP s without requiring some special property of the matrix coefficient matrix. Our aim is to construct some interior point algorithms which, according to the duality theorem in EP form, gives a solution of the original problem or detects the lac...