Semidefinite Programming Relaxation vs Polyhedral Homotopy ...

Discretization of Mimura’s ODE with 2 unknowns u, v : [0, 5] → Ru xx = −(20/9)(35 + 16u − u 2 )u + 20uv,v xx = (1/4)((1 + (2/5)v)v − uv),u x (0) = u x (5) = v x (0) = v x (5) = 0,Discretize:x i = i∆x (i = 0, 1, 2,... ), u x (x i ) ≈ (u(x i+1 ) − u(x i−1 ))/(2∆x).Numerical results on SparsePOP∆x n obj.funct. relax. order r cpu1.0 8 ∑ r i u(x i ) ↑ 3 11.30.5 18 ∑ r i u(x i ) ↑ 3 57.8Here r i ∈ (0, 1) : random numbers.Workshop on Advances in Optimization, April 19-21, 2007 – p.18/24