Rongqin Sheng

A Superlinearly Convergent Primal-Dual Infeasible-Interior-Point Algorithm for Semidefinite Programming

A primal-dual infeasible-interior-point path-following algorithm is proposed for solving semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible, the algorithm finds an optimal solution in at most

A Large-Step Infeasible-Interior-Point Method for the P * -Matrix LCP

O(\sqrt{n}L)

Predictor-corrector algorithm for solving P * (k)-matrix LCP from arbitrary positive starting points

iterations, where n is the size of the problem and L is the logarithm of the ratio of the initial error and the tolerance. If the starting point is large enough, then the algorithm terminates in at most O(nL) steps either by finding a solution or by determining that the primal-dual problem has no solution of norm less than a given number. Moreover, we propose a sufficient condition for the superlinear convergence of the algorithm. In addition, we give two special cases of SDP for which the algorithm is quadratically convergent.

On the Local Convergence of a Predictor-Corrector Method for Semidefinite Programming

A large-step infeasible-interior-point method is proposed for solving

A Quadratically Convergent Infeasible-Interior-Point Algorithm for LCP with Polynomial Complexity

P_*(\k)

A path following method for LCP withsuperlinearly convergent iteration sequence

-matrix linear complementarity problems. It is new even for monotone LCP. The algorithm generates points in a large neighborhood of an infeasible central path. Each iteration requires only one matrix factorization. If the problem is solvable, then the algorithm converges from arbitrary positive starting points. The computational complexity of the algorithm depends on the quality of the starting point. If a well-centered starting point is feasible or close to being feasible, then it has

A predictor-corrector method for solving the P*(k)-matrix lcp from infeasible starting points

O((1+\k)\sqrt{n}\ln(\eps_0/\eps))

Nonsymmetric Search Directions for Semidefinite Programming

-iteration complexity. With appropriate initialization, a modified version of the algorithm terminates in

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

O((1+\k)^2n\ln(\eps_0/\eps))

A Large-Step Infeasible-Interior-Point Method for the P

steps either by finding a solution or by determining that the problem is not solvable. High-order local convergence is proved for problems having a strictly complementary solution. We note that while the properties of the algorithm (e.g., computational complexity) depend on