Self-Scaled Barrier Functions on Symmetric Cones and Their Classification
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چکیده
منابع مشابه
Numerical Analysis Reports SELF–SCALED BARRIER FUNCTIONS ON SYMMETRIC CONES AND THEIR CLASSIFICATION
Self–scaled barrier functions on self–scaled cones were introduced through a set of axioms in 1994 by Y. E. Nesterov and M. J. Todd as a tool for the construction of long–step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of definition, and subsequently their...
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Self{scaled barrier functions on self{scaled cones were introduced through a set of axioms in 1994 by Y. E. Nesterov and M. J. Todd as a tool for the construction of long{step interior point algorithms. This paper provides rm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of deenition, and subsequently their de...
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Self–scaled barrier functions are fundamental objects in the theory of interior–point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self–scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with...
متن کاملSelf-Scaled Barriers for Irreducible Symmetric Cones
Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...
متن کاملSelf-Scaled Barrier Functions: Decomposition and Classi cation
The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. Nesterov and Todd's concept of self-scaled barrier functionals allows the exploitation of algebraic and geometric properties of symmetric cones in certain variants of the barrier method applied...
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عنوان ژورنال:
- Foundations of Computational Mathematics
دوره 2 شماره
صفحات -
تاریخ انتشار 2002