Technical Note—Some Examples Concerning Linear Continuity of Solutions to Programming Problems

Abstract

In this note we construct some counterexamples concerning upper semicontinuity and linear upper and lower semicontinuity of the solution sets and ϵ-solution sets of nonlinear programming programs: max f ( x ), subject to g ( x ) ≦ b . These examples answer some of the questions in a recent paper by Stern and Topkis.