The IPNLP solver in the OPTMODEL procedure enables you to solve general nonlinear programming problems. Mathematically, a general nonlinear programming problem can be stated as
where is the nonlinear objective function and is the set of general nonlinear equality and inequality constraints. The lower and upper bounds on the decision variable are denoted by l and u, respectively.
The IPNLP solver implements a primal-dual interior point algorithm that includes several powerful features from recent state-of-the-art algorithms. It uses a line-search procedure and a merit function to ensure convergence of the iterates to a local minimum.
The IPNLP solver iteratively generates better approximations of the primal variables and the dual variables. The solver also ensures that the primal iterates always remain strictly within their bounds for every iteration.
The IPNLP solver is particularly suited for problems that contain many dense nonlinear inequality constraints, and it is expected to outperform solvers that use other NLP solution techniques.