A PRACTICAL INTERIOR-POINT METHOD FOR CONVEX-PROGRAMMING

The authors present a primal interior-point algorithm for solving conv ex programs with nonlinear constraints. The algorithm uses a predictor -corrector strategy to follow a smooth path that leads from a given st arting point to an optimal solution. A convergence analysis is given s howing that under mild assumptions the algorithm simultaneously iterat es towards feasibility and optimality. The matrices involved can be ke pt sparse if the nonlinear functions are separable or depend on only a few variables. A preliminary implementation has been developed. Some promising numerical results indicate that the algorithm may be efficie nt in practice, and that it can deal in a single phase with infeasible starting points without relying on some ''big M'' parameter.