We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iterat...We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.展开更多
In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a f...In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a full Nesterov-Todd step and the strategy of the central path to obtain a solution of symmetric optimization.We establish the iteration bound for the algorithm,which matches the currently best-known iteration bound for these methods,and prove that the algorithm is quadratically convergent.展开更多
文摘We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.
基金The author is grateful to the two anonymous referees and the Editors for theirconstructive comments and suggestions to improve the presentation.
文摘In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a full Nesterov-Todd step and the strategy of the central path to obtain a solution of symmetric optimization.We establish the iteration bound for the algorithm,which matches the currently best-known iteration bound for these methods,and prove that the algorithm is quadratically convergent.
