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- Antoine Deza, Tamás Terlaky, Yuriy Zinchenko
- Oper. Res. Lett.
- 2008

By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities deflning the polytope.… (More)

- Millie Chu, Yuriy Zinchenko, Shane G. Henderson, Michael B. Sharpe
- Physics in medicine and biology
- 2005

The recent development of intensity modulated radiation therapy (IMRT) allows the dose distribution to be tailored to match the tumour's shape and position, avoiding damage to healthy tissue to a… (More)

- Antoine Deza, Tamás Terlaky, Yuriy Zinchenko
- Discrete & Computational Geometry
- 2009

The curvature of a polytope, defined as the largest possible total curvature of the associated central path, can be regarded as a continuous analogue of its diameter. We prove an analogue of the… (More)

We consider a family of linear optimization problems over the ndimensional Klee-Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This… (More)

- Yuriy Zinchenko
- Optimization Letters
- 2008

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = ∏ i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for R+. We… (More)

It has come to the attention of the authors that the MATLAB code1 provided in the original paper does not work as stated. Although the code presented in the original paper was only intended to act as… (More)

- Yuriy Zinchenko
- 2010

Hyperbolic Programming (HP) –minimizing a linear functional over an affine subspace of a finite-dimensional real vector space intersected with the so-called hyperbolicity cone– is a class of convex… (More)

- Masoud Zarepisheh, Mohammad Shakourifar, +7 authors Yuriy Zinchenko
- Physics in medicine and biology
- 2013

The dose-volume histogram (DVH) is a clinically relevant criterion to evaluate the quality of a treatment plan. It is hence desirable to incorporate DVH constraints into treatment plan optimization… (More)

Radiation therapy is an important modality in treating various cancers. Various treatment planning and delivery technologies have emerged to support Intensity Modulated Radiation Therapy (IMRT),… (More)

We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This… (More)