# An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Optimization

@article{Kheirfam2015AnAI,
title={An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Optimization},
author={Behrouz Kheirfam},
journal={Journal of Mathematical Modelling and Algorithms in Operations Research},
year={2015},
volume={14},
pages={55-66}
}
• B. Kheirfam
• Published 1 March 2015
• Computer Science
• Journal of Mathematical Modelling and Algorithms in Operations Research
We present an adaptive full Nesterov-Todd step infeasible interior-point method for semidefinite optimization. The proposed algorithm requires two types of full Nesterov-Todd steps are called, feasibility steps and centering steps, respectively. At each iteration both feasibility and optimality are reduced exactly at the same rate. In each iteration of the algorithm we use the largest possible barrier parameter value θ. The value θ varies from iteration to iteration and it lies between the two…
3 Citations

### A Wide Neighborhood Second-order Predictor-corrector Interior-point Algorithm for Semidefinite Optimization with Modified Corrector Directions

• Computer Science
Fundam. Informaticae
• 2017
The algorithm is based on the wide neighborhood of the central path and modified corrector directions, and the iteration complexity bound is O( √ n log X •S ) for the Nesterov-Todd direction, which coincides with the best known complexity results for semidefinite optimization.

### An predictor–corrector interior-point algorithm for semidefinite optimization based on a wide neighbourhood

• Mathematics
Int. J. Comput. Math.
• 2021
This paper shows that, in addition to the predictor step, each corrector step decreases the duality gap as well, and proves that the iteration complexity of the proposed algorithm coincides with the best iteration bound for small neighbourhood algorithms that use the Nesterov–Todd direction.

## References

SHOWING 1-10 OF 40 REFERENCES

### A New Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semi-Definite Optimization

A new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization that converges and finds an approximate solution in polynomial time is presented.

### A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function

The iteration bound coincides with the best iteration bound for infeasible interior-point methods, that is, $O(r\log\frac{r}{\epsilon})$, where $r$ is the rank of Euclidean Jordan algebra.

### A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization

• Mathematics, Computer Science
J. Optim. Theory Appl.
• 2013
An infeasible interior-point method for linear optimization to second-order conic optimization is generalized and finds a solution in a finite number of iterations or determines that the primal–dual problem pair has no optimal solution with vanishing duality gap.

### Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step

• B. Kheirfam
• Computer Science, Mathematics
Numerical Algorithms
• 2011
A primal-dual infeasible interior-point algorithm that uses full Nesterov-Todd steps with a different feasibility step is proposed, and the currently best known iteration bound for semidefinite optimization problems is obtained.

### Simplified analysis for full-Newton step infeasible interior-point algorithm for semidefinite programming

• Computer Science
• 2013
An analysis of the full-Newton step infeasible interior-point algorithm for semidefinite optimization, which is an extension of the algorithm introduced by Roos, where I is an identity matrix and V is a symmetric positive definite matrix.

### A New Full Nesterov–Todd Step Primal–Dual Path-Following Interior-Point Algorithm for Symmetric Optimization

• Mathematics, Computer Science
J. Optim. Theory Appl.
• 2012
This paper generalizes a primal–dual path-following interior-point algorithm for linear optimization to symmetric optimization by using Euclidean Jordan algebras and derives the currently best known iteration bound for the small-update method.

### A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem

• Mathematics
• 2014
A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types