A New Karmarkar-Based Algorithm for Optimizing Convex, Non- Linear Cost Functions with Linear Constraints

In this talk, we derive and implement a new Karmarkar-based algorithm for minimizing convex, non-linear cost functions subject to linear constraints. Our algorithm combines the centering scheme of Karmarkar's algorithm with Newton's second order method. The new algorithm converges fast even when the objective function is poorly conditioned, and all the variables are non-negative. We present numerical results from a number of small sample problems which compare the convergence rates for the Karmarkar projected gradient method, the Newton second order method utilizing an active sets approach, anf our new algorithm. In all cases our algorithm took fewer iterations to converge.