NLP Sensitivity Analysis for RHS Perturbations. A Brief Survey and Second-Order Extensions.
Interim technical rept.,
GEORGE WASHINGTON UNIV WASHINGTON D C INST FOR MANAGEMENT SCIENCE AND ENGINEERING
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The paper first presents a brief historical survey of the introduction of Lagrange multipliers in characterizing optimality and duality in mathematical programming. Attention is focused on the interpretation of optimal Lagrange multipliers as a first-order measure of the sensitivity of the optimal value function of the problem with right-hand side perturbations of the constraints. For the latter problem, explicit formulas are then obtained for calculating the first derivatives of a Kuhn-Tucker triple, resulting in second-order characterizations of the optimal value function. Approximation formulas are developed for the algorithm based on the logarithmic-quadratic penalty function. Applications are indicated, e.g., in obtaining sharper estimates of the optimal value of a problem with different constraint right-hand sides, in applying a well known approach to solving a class of large-scale decomposable nonlinear programming problems, and in supplementing the rich theoretical developments associated with a first-order analysis of the optimal value function of the problem with perturbations in the right-hand sides of the constraints. Author
- Numerical Mathematics