Maximizing perturbation radii for robust convex quadratically constrained quadratic programs

Under the assumption that uncertain coefficients corresponding to each constraint are perturbed in an ellipsoidal set, we consider the problem of maximizing the perturbation radius of the ellipsoidal set associated to a robust convex quadratically constrained quadratic programming problem to maintain some properties of a pre-decision. To this end, a fractional programming problem is first formulated to solve the problem, and then equivalently reformulated into linear conic programs over positive semi-definite, second-order cones that are solvable in polynomial time. Numerical experiments in connection with the robust Markowitz's portfolio selection problem are provided to demonstrate the proposed concept of sensitivity analysis. Additionally, certain numerical results are also presented to compare the efficiency of direct solutions of the proposed linear conic programs with that of a bisection method for the corresponding fractional programming problem. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study examines the maximization of perturbation radius of an ellipsoidal set under perturbed uncertain coefficients for each constraint, in the context of robust convex quadratically constrained quadratic programming problems. By formulating a fractional programming problem and reformulating it into linear conic programs solvable in polynomial time, the proposed sensitivity analysis concept is demonstrated through numerical experiments related to robust Markowitz's portfolio selection. Comparative numerical results show the efficiency of direct solutions of linear conic programs versus a bisection method for the corresponding fractional programming problem.