Sensitivity analysis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of simultaneous perturbation. Criteria for convexity, concavity or linearity of the optimal value function on invariancy intervals are derived. Furthermore, differentiability of the optimal value function is studied, and linear optimization problems are given to calculate the left and right derivatives. An algorithm, that is capable to compute the transition points and optimal partitions on all invariancy intervals, is outlined. We specialize the method to Linear Optimization problems and provide a practical example of simultaneous perturbation parametric quadratic optimization problem from electrical engineering.