A geodesic interior-point method for linear optimization over symmetric cones

Understand

We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming.

• In contrast to classical IPMs, we update iterates with a geodesic of the cone instead of the kernel of the linear constraints.
• This approach yields a primal-dual-symmetric, scale-invariant, and line-search-free algorithm that uses just half the variables of a standard primal-dual IPM.
• With elementary arguments, we establish polynomial-time convergence matching the standard square-root-n bound.