Topics in matrix analysis
A class of projective transformations for linear programming
SIAM Journal on Computing
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
On quadratic and OnL convergence of a predictor-corrector algorithm for LCP
Mathematical Programming: Series A and B
SIAM Review
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
On the Nesterov--Todd Direction in Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Hi-index | 7.29 |
In this paper, we extend the Ai-Zhang predictor-corrector method to the class of semidefinite programming. First, we define a new wide neighborhood N(@t,@b). Another key ingredient of our method is that we treat the classical Newton direction as the sum of two other directions, corresponding to respectively the negative part and the positive part of the right-hand-side. We prove that, besides the predictor steps, each corrector step also reduces the duality gap by a rate of 1-1O(n). Then the method enjoys the low iteration bound of O(nL), which is better than that of usual wide neighborhood algorithm O(nL), where n is the dimension of the problem and L=(X^0)^T*S^0@e with @e the required precision and (X^0,y^0,S^0) the initial interior solution.