A Quasi-Newton Method with Rank-Two Update to Solve Interval Optimization Problems

In this study, a quasi-Newton method is developed to obtain efficient solutions of interval optimization problems. The idea of generalized Hukuhara differentiability for multi-variable interval-valued functions is employed to derive the quasi-Newton method. Through an inverse-Hessian approximation with rank-two modification, the proposed technique sidesteps the high computational cost for the computation of inverse-Hessian in Newton method for interval optimization problems. The rank-two modification of inverse-Hessian approximation is applied to generate the iterative points in the quasi-Newton technique. A sequential algorithm and the convergence result of the derived method are also presented. It is obtained that the sequence in the proposed method has superlinear convergence rate. The method is also found to have quadratic termination property. Two numerical examples are provided to illustrate the developed technique. © 2016, Springer India Pvt. Ltd.