Solution continuity in variational conditions

Authors:
Stephen M. Robinson;Shu Lu
Affiliations:
Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, USA 53706-1572;Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, USA 53706-1572
Venue:
Journal of Global Optimization
Year:
2008

Citing 0
Cited 2

Descent methods for a class of generalized variational inequalities

Computational Optimization and Applications
Korpelevich's method for variational inequality problems in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present some results about Lipschitzian behavior of solutions to variational conditions when the sets over which the conditions are posed, as well as the functions appearing in them, may vary. These results rely on calmness and inner semicontinuity, and we describe some conditions under which those conditions hold, especially when the sets involved in the variational conditions are convex and polyhedral. We then apply the results to find error bounds for solutions of a strongly monotone variational inequality in which both the constraining polyhedral multifunction and the monotone operator are perturbed.