= Primal-dual interior-point method
A <primal-dual interior-point method> solves perturbed <KKT conditions> while updating both the primal variables and <Lagrange multipliers>. For inequalities written as $c_i\geq0$, a logarithmic-barrier path has positive $c_i,y_i$ and perturbed complementarity $c_iy_i=\mu$. A <Newton system> for these coupled equations gives primal and dual corrections together, with damping to preserve positivity. This can avoid explicitly forming the most ill-conditioned eliminated barrier Hessian, although scaling and regularity still matter.
Back to article page
