Primal–dual and primal interior point algorithms for general nonlinear programs

An interior point algorithm for general nonlinear programs is presented. Inequality constraints are converted to equalities with slack variables. All bounds are handled with a barrier term in the objective. The Kuhn–Tucker system of the resulting equality constrained barrier problem is solved directly by Newton's Method. Primal–Dual, Primal, and Primal–Dual with trust region variants are developed and evaluated. An implementation which utilizes the true Lagrangian Hessian and exploits Jacobian and Hessian sparsity is described. Computational results are presented and discussed.