On the Convergence of Central Path and Generalized Proximal Point Method for Symmetric Cone Linear Programming

Abstract

Abstract:In this paper, we consider the symmetric cone linear programming(SCLP), by using the Jordan-algebraic technique, we extend the generalized proximal point method in linear programming and semidefinite programming to the SCLP. Under some reasonable conditions, we obtain the convergence of primal central paths associated to the symmetric cone distance function.

Derivatives of eigenvalues and Jordan frames

“…Euclidean Jordan algebras have been used to deal with optimization problems involving symmetric cones (cf. [4,5,7,6,8,9,10,11,15,16,12,13,19,18,20,21,22]). The optimization problems involving symmetric cones are tractable ones.…”