Interior point method

This is the nonlinear optimization problem in Primal-dual interior point method.

minimize f(x), subject to ci(x)≧0 for i=1,2,..,m , x∈Rn, f:Rn→R, ci∈Rn→R

x is a Lagrange multiplier.

ci(x)λ=μ, ∀i=1,2,..,m , λ∈Rm

F(X0)≧F(x1)≧F(X2)≧...

F is minimal and the bottom.