First-Order Sensitivity of Linearly Constrained Strongly Monotone Composite Variational Inequalities ⁄
Jong‐Shi Pang, Defeng Sun · 2008
Extending the characterization of the directional derivatives of a strongly regular solution to a variational inequality under parameter perturbations, this paper derives a first-order sensitivity result for a monotone-plus affine variational inequality (AVI) having non-isolated solutions. The result employs a “directional AVI ” whose solutions provide the directional derivatives, if they exist, of some invariant constants of the original AVI when its data are perturbed. Solvability of the directional AVI is characterized in terms of the direction of data perturbation. An application of this result to the support-vector machine quadratic program is discussed. An extension to a linearly constrained variational inequality defined by a strongly monotone composite mapping is also addressed. 1