T-Forward Method: A Closed-Form Solution and Polynomial Time Approach for Convex Nonlinear Programming

We present a closed-form solution for convex Nonlinear Programming (NLP). It is closed-form solution if all the constraints are linear, quadratic, or homogeneous. It is polynomial when applied to convex NLP. It gives exact optimal solution when applied to LP. The T-forward method moves forward inside the feasible region with a T-shape path toward the increasing direction of the objective function. Each T-forward move reduces the residual feasible region at least by half. The T-forward method can solve an LP with 10,000 variables within seconds, while other existing LP algorithms will take millions of years to solve the same problem if run on a computer with 1GHz processor.