1. |
Yotaro Takazawa, Shinji Mizuno, Tomonari Kitahara, Approximation algorithms for the covering-type k-violation linear program, *Optimization Letters*, https://doi.org/10.1007/s11590-019-01425-w, 2019.04. |

2. |
Masaya Tano, Ryuhei Miyashiro and Tomonari Kitahara, Steepest-edge rule and its number of simplex iterations for a nondegenerate LP, *Operations Research Letters*, 47, 3, 151-156, 2019.05. |

3. |
Tomonari Kitahara and Noriyoshi Sukegawa, A simple projection algorithm for linear programming problems, *Algorithmica*, 10.1007/s00453-018-0436-3, 2018.03, Fujishige et al. propose the LP-Newton method, a new algorithm for linear programming problem (LP). They address LPs which have a lower and an upper bound for each variable, and reformulate the problem by introducing a related zonotope. The LP-Newton method repeats projections onto the zonotope by Wolfe’s algorithm. For the LP-Newton method, Fujishige et al. show that the algorithm terminates in a finite number of iterations. Furthermore, they show that if all the inputs are rational numbers, then the number of projections is bounded by a polynomial in L, where L is the input length of the problem. In this paper, we propose a modification to their algorithm using a binary search. In addition to its finiteness, if all the inputs are rational numbers and the optimal value is an integer, then the number of projections is bounded by L+1, that is, a linear bound.. |

4. |
Tomonari Kitahara and Takashi Tsuchiya, An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming, *Optimization Methods and Software*, 33, 1-25, 2018.03. |

5. |
Yotaro Takazawa, Shinji Mizuno, Tomonari Kitahara, An improved approximation algorithm for the covering 0–1 integer program, *Pacific Journal of Optimization*, 2017.12. |

6. |
Bruno F. Lourenço, Tomonari Kitahara, Masakazu Muramatsu and Takashi Tsuchiya , An extension of Chubanov’s algorithm to symmetric cones, *Mathematical Programming*, 10.1007/s10107-017-1207-7, 2017.11, In this work we present an extension of Chubanov’s algorithm to the case of homogeneous feasibility problems over a symmetric cone K. As in Chubanov’s method for linear feasibility problems, the algorithm consists of a basic procedure and a step where the solutions are confined to the intersection of a half-space and K . Following an earlier work by Kitahara and Tsuchiya on second order cone feasibility problems, progress is measured through the volumes of those intersections: when they become sufficiently small, we know it is time to stop. We never have to explicitly compute the volumes, it is only necessary to keep track of the reductions between iterations. We show this is enough to obtain concrete upper bounds to the minimum eigenvalues of a scaled version of the original feasibility problem. Another distinguishing feature of our approach is the usage of a spectral norm that takes into account the way that K is decomposed as simple cones. In several key cases, including semidefinite programming and second order cone programming, these norms make it possible to obtain better complexity bounds for the basic procedure when compared to a recent approach by Peña and Soheili. Finally, in the appendix, we present a translation of the algorithm to the homogeneous feasibility problem in semidefinite programming.. |

7. |
Yotaro Takazawa, Shinji Mizuno, and Tomonari Kitahara, An approximation algorithm for the partial covering 0-1 integer program, *Discrete Applied Mathematics*, 10.1016/j.dam.2017.08.024, 2017.09. |

8. |
Noriyoshi Sukegawa and Tomonari Kitahara, A refinement of Todd's bound for the diameter of a polyhedron, *Operations Research Letters*, 43, 534-536, 2015.09. |

9. |
Tomonari Kitahara and Shinji Mizuno, The simplex method and 0-1 polytopes, *Journal of Mathematical Sciences*, 2, 17-21, 2015.01. |

10. |
Tomonari Kitahara and Shinji Mizuno, On the number of solutions generated by the simplex method for LP, *Optimization and Control Techniques and Applications, Springer Proceedings in Mathematics & Statistics*, 86, 75-90, 2014.06. |

11. |
Tomonari Kitahara, Shinji Mizuno, and Jianming Shi, The LP-Newton method for standard form linear programming problems, *Operations Research Letters*, 41, 426-429, 2013.09. |

12. |
Tomonari Kitahara and Takashi Tsuchiya, A simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm and its objective-function-free complexity, *SIAM Journal on Optimization*, 23, 1890-1903, 2013.09. |

13. |
Tomonari Kitahara and Shinji Mizuno, An upper bound for the number of different solutions generated by the primal simplex method with any selection rule of entering variables, *Asia-Pacific Journal of Operational Research*, 10.1142/S0217595913400125, 30, 2013.06. |

14. |
Tomonari Kitahara and Shinji Mizuno, A bound for the number of basic solutions generated by the simplex method, *Mathematical Programming*, 137, 579-586, 2013.02. |

15. |
Tomonari Kitahara, Tomomi Matsui, and Shinji Mizuno, On the number of solutions generated by Dantzig's simplex method for LP with bounded variables, *Pacific Journal of Optimization*, 8, 447-455, 2012.07. |

16. |
Tomonari Kitahara and Shinji Mizuno, On the number of solutions generated by the dual simplex method, *Operations Research Letters*, 40, 172-174, 2012.05. |

17. |
Tomonari Kitahara and Shinji Mizuno, Lower bounds for the maximum number of solutions generated by the simplex method, *Journal of the Operations Research Society of Japan*, 54, 191-200, 2011.06. |

18. |
Tomonari Kitahara and Shinji Mizuno, Klee-Minty's LP and upper bounds for Dantzig's simplex method, *Operations Research Letters*, 39, 88-91, 2011.03. |

19. |
Tomonari Kitahara and Takashi Tsuchiya, Proximity of weighted and layered least squares solutions, *SIAM Journal on Matrix Analysis and Applications*, 1172-1186, 2009.09. |

20. |
Tomonari Kitahara, Shinji Mizuno, and Kazuhide Nakata, Quadratic and convex minimax classification problems, *Journal of the Operations Research Society of Japan*, 51, 191-201, 2008.06. |