A Modified Super Convergent Line Search Algorithm for Solving Quadratically Constrained Quadratic Optimization Problems

Abstract

In this paper, a modified super convergence line search algorithm is introduced to address the use of the optimal support points of the segmented design space and the bias to evaluate the optimal step length in a quadratically constrained quadratic optimization problem. The optimum number of segments and the minimum number of iterations are considered and the method modified the algorithm by linearising the quadratic constraint through the partial derivative of the Jacobian function to attained optimal step-length and convergence. The new algorithm was applied to two quadratically constrained problems and the results indicated that the modified algorithm satisfied the convergent criteria in six and one iteration and achieved the optimal solutions in both problem set respectively. This shows the effectiveness of the modified algorithm in solving quadratically constrained quadratic optimization problems.