Title: Invariance and Efficiency in Convex Representations

Many optimization problems can be "converted" to semidefinite optimization problems. In particular, every homogeneous cone can be expressed as the intersection of the cone of symmetric positive semidefinite matrices and a linear subspace. Some other convex cones can be dealt with in a similar way using linear maps, linear projections and the positive semidefiniteness requirements.
In this talk, I will focus on two lines of investigations:
1. Ways of evaluating the quality of representations from a theoretical viewpoint.
2. Ways of utilizing the representations as theoretical tools in establishing original facts about more complicated cones.
This talk is based on joint work with Chek Beng Chua.