An efficient algorithm for convex quadratic semi-definite optimization
Lipu Zhang Yinghong Xu Zhengjing Jin
Numerical Algebra, Control & Optimization 2012, 2(1): 129-144 doi: 10.3934/naco.2012.2.129
We present a full-step interior-point algorithm for convex quadratic semi-definite optimization based on a simple univariate function. The algorithm uses the simple function to determine the search direction and define the neighborhood of central path. The full-step used in the algorithm has local quadratic convergence property according to the proximity function which is also constructed by the simple function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bounds for convex quadratic semi-definite optimization.
keywords: complexity analysis. Convex quadratic semi-definite optimization interior point algorithm
A full-modified-Newton step infeasible interior-point algorithm for linear optimization
Yinghong Xu Lipu Zhang Jing Zhang
Journal of Industrial & Management Optimization 2016, 12(1): 103-116 doi: 10.3934/jimo.2016.12.103
Based on an equivalent reformulation of the central path, we obtain a modified-Newton step for linear optimization. Using this step, we propose an infeasible interior-point algorithm. The algorithm uses only one full-modified-Newton step search in each iteration. The complexity bound of the algorithm is the best known for infeasible interior-point algorithm.
keywords: modified-Newton-direction linear optimization complexity analysis. Infeasible interior-point algorithm full-Newton step

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