Physarum Polycephalum is a Slime mold that can solve the shortest path problem. A mathematical model based on the Physarum's behavior known as the Physarum Directed Dynamics can solve positive linear programs. In this talk, we will try to extend this dynamic's ability to figure out a novel way to solve Semi-Definite Programming (SDP) problems that are harder than linear programs, and our goal is to prove this dynamic converges to the optimum answer of this optimization problem. Empirical results suggest the proposed extension of the dynamic can solve the SDP showing that this nature-inspired algorithm can solve one of the hardest problems in the polynomial domain.