euclidean jordan algebras – Optimization Online

E. Lieb convexity inequalities and noncommutative Bernstein inequality in Jordan-algebraic setting

Published: 2014/08/14, Updated: 2022/05/13

Generalized Convexity/Monoticity, Other Topics euclidean jordan algebras, generalized convexity, quantum entropy

We describe a Jordan-algebraic version of E. Lieb convexity inequalities. A joint convexity of Jordan-algebraic version of quantum entropy is proven. SA spectral theory on semi-simple complex Jordan algebras is used as atool to prove the convexity results. Possible applications to optimization and statistics are indicated CitationPreprint, University of Notre Dame, August 2014ArticleDownload View PDF

On Hazan’s algorithm for symmetric programming problems

Published: 2013/01/30

Leonid Faybusovich

Approximation Algorithms, Linear, Cone and Semidefinite Programming euclidean jordan algebras, low-rank approximations to optimal solutions, symmetric programming

We describe the generalization of Hazan’s algorithm for symmetric programming problems CitationNotre Dame Report, December, 2012ArticleDownload View PDF

Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric Cones

Published: 2004/04/05

Bharath Kumar Rangarajan

Linear, Cone and Semidefinite Programming, Nonlinear Optimization euclidean jordan algebras, infeasible-interior-point methods, polynomial convergence, symmetric cones

We establish polynomial-time convergence of infeasible-interior-point methods for conic programs over symmetric cones using a wide neighborhood of the central path. The convergence is shown for a commutative family of search directions used in Schmieta and Alizadeh. These conic programs include linear and semidefinite programs. This extends the work of Rangarajan and Todd, which established … Read more

Self-scaled barriers for irreducible symmetric cones

Published: 2001/04/10

Raphael Hauser

Yongdo Lim

Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming euclidean jordan algebras, interior point methods, self-scaled barrier functions, semidefinite programming, 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 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 a decomposition … Read more