Chapter 5 Superlinear Bracketing Based Lambda Method for Quadratic Objective Optimization Problem with Non-linear Equality Constraint

Various mathematical programming methods are developed in the literature for solving quadratic objective optimization problem. Conventional approaches such as Lambda iteration method, gradient method and quadratic programming method are used to solve the quadratic objective optimization problems. These conventional methods have different drawbacks of their own. In Lambda iteration method, it is difficult to adjust Lambda and more number of iterations are required for the convergence. The gradient method is only a quasi-optimal scheme based on the hill climbing method. Quadratic programming is an effective method to find the global optimal solution for optimization problems having quadratic objective and linear constraints. A variety of problems in different fields of science and technology require to find the solution of non-linear equation. The aim of developing iterative methods for solving non-linear equations is to attain the solution as fast a possible with minimum computational costs. Mullers method (Barrodale and Wilson, 1978),