Nonlinear Programming Sensitivity Analysis Results Using Strong Second Order Assumptions.

Abstract : Invoking conditions utilized to obtain numerous ideal results in nonlinear programming, this paper summarizes the development of a basis for calculating the first partial derivatives of a Kuhn-Tucker triple and the first and second partial derivatives of the optimal value function, with respect to problem parameters. In the context of prior results, a simpler but much more general derivation of the Kuhn-Tucker triple derivatives is presented, and a more concise formula for the Hessian of the optimal value function is given. Particularizations to the problems with right-hand-side constraint perturbations, no constraint perturbations and no constraints follow easily and are briefly treated. Further extensions and applications are indicated. (Author)