A smooth counterexample to pointwise strong-duality claims for mathematical programs with equilibrium constraints

This independent technical note examines the pointwise strong-duality statements in Singh, Mishra and Hamdi, “A Duality Framework for Mathematical Programs with Tangential Subdifferentials” (Algorithms 19(1), 2026, 45; DOI: 10.3390/a19010045). A smooth two-variable polynomial construction satisfies the stated assumptions at a global and strict local primal minimizer, including GS-ACQ, while the displayed Wolfe and Mond–Weir duals both have maximum 1 and the primal minimum is 0. The construction survives correction of the apparent complementarity-multiplier typo. The note also corrects the tangential subdifferentials in Example 1 and distinguishes the strong-duality counterexample from weak duality under its full hypotheses. Files: revised four-page PDF and ZIP containing the PDF, editable LaTeX source, exact arithmetic verification script and README. AI disclosure: OpenAI ChatGPT was used for English-language improvement, computational checks, and assistance with mathematical analysis and drafting. The author assumes full responsibility for the construction and verification of counterexamples, proofs, and all mathematical statements.