Numerical Solution of Optimization Problems Via Multiplier Method

This paper discusses the use of conjugate gradient algorithm and Modified Newton’s method employed to determine the Solution of equality constrained optimization problems. The conjugate gradient algorithm was used as a scaling factor with the purpose of making the initial guess to be closer to the optimal solution, after which the Newton’s method was introduced to guide against jumping the optimal points and ill-conditioning of the problems along the search path. A Lagrange multiplier Vector updating scheme at each one-dimensional search is considered. It was proved using some tested problems that the rate of convergence of the method is linear and lesser number of iterations will be generated if one starts with sufficiently small penalty factor.