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- Osman Güler
- Math. Oper. Res.
- 1997

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial… (More)

- Osman Güler
- Math. Oper. Res.
- 1996

We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for… (More)

- Yinyu Ye, Osman Güler, Richard A. Tapia, Yin Zhang
- Math. Program.
- 1993

- Osman Güler
- SIAM Journal on Optimization
- 1992

- Osman Güler
- Math. Oper. Res.
- 1993

A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We… (More)

- Osman Güler, Levent Tunçel
- Math. Program.
- 1998

We characterize the barrier parameter of the optimal self{concordant barriers for homogeneous cones. In particular, we prove that for homogeneous convex cones this parameter is the same as the rank of the corresponding Siegel domain. We also provide lower bounds on the barrier parameter in terms of the Carath eodory number of the cone. The bounds are tight… (More)

- Osman Güler, Yinyu Ye
- Math. Program.
- 1993

- Osman Güler, Alan J. Hoffman, Uriel G. Rothblum
- SIAM J. Matrix Analysis Applications
- 1995

- Osman Güler, Filiz Gürtuna
- Optimization Methods and Software
- 2012

A convex body K in R has around it a unique circumscribed ellipsoid CE(K) with minimum volume, and within it a unique inscribed ellipsoid IE(K) with maximum volume. The modern theory of these ellipsoids is pioneered by Fritz John in his seminal 1948 paper. This paper has two, related goals. First, we investigate the symmetry properties of a convex body by… (More)