Computable Optimal Value Bounds and Solution Vector Estimates for General Parametric NLP Programs

摘要

A simple technique is proposed for calculating piecewise-linear continuous global upper and lower parametric bounds on the optimal value of nonlinear parametric programs that have a convex or concave optimal value function. This provides a procedure for calculating parametric optimal value bounds for general nonconvex parametric programs, whenever convex or concave underestimating or overestimating problems can be constructed. For the jointly convex program, this approach leads immediately to the construction of a parametric feasible vector yielding a computable and generally sharper nonlinear optimal value upper parametric bound. Connections and extensions of well-known duality results are developed that lead to constructive interpretations of the bounds results and generally sharper nonlinear parametric lower bounds. (Author)