Perturbed minimization, with constraints adjoined or deleted
B.I. Craven · Mathematische Operationsforschung und Statistik Series Optimization · 1983
A perturbed constrained nonlinear minimization problem is considered, in spaces of arbitrary dimensions, without convexity or compactness hypotheses. Under some assumptions about the perturbed minimum, the Fréchet derivative of the perturbed optimal objective function is related to the Lagrangian for the problem. This result allows bounds to be calculated for the effect of deleting some constraints. This applies, in particular, to the truncation of a semi-infinite programming problem to a finite dimensional, and thus computable, problem. Bounds for adjoining constraints, or deleting variables, are also obtained, under further assumptions.