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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.

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