Exact certificates of positivity for polynomials with rational coefficients

Computation of solutions to polynomial optimization and variational inequality problems

Topological properties of solution sets in convex vector optimization and monotone vector variational inequality

Vu Trung Hieu, Alfredo Noel Iusem, Paul Hugo Schmölling, Akiko Takeda, Univariate representations of solutions to generic polynomial complementarity problems,  Journal of Optimization Theory and Applications, (2025)

Vu Trung Hieu, Akiko Takeda, Computing local minimizers in polynomial optimization under genericity conditions, Journal of Global Optimization, (2025)

Vu Trung Hieu, Elisabeth Anna Sophia Köbis, Markus Arthur Köbis, Paul Hugo Schmölling, Unboundedness of the images of set-valued mappings having closed graphs: Application to vector optimization, Journal of Global Optimization, 91, pages 217–234 (2025)

Victor Magron, Mohab Safey El Din, Trung-Hieu Vu: Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients, SIAM Journal on Optimization,  33, pages 63-88 (2023)

Vu Trung Hieu: On the Nonemptiness and Boundedness of Solution Sets of Weakly Homogeneous Optimization Problems, Set-Valued and Variational Analysis, 30, pages 1105-1116 (2022)

Victor Magron, Mohab Safey El Din, Markus Schweighofer, Trung-Hieu Vu: Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients, Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, pages 325–332 (2022)

Vu Trung Hieu: On the solution existence and stability of polynomial optimization problems, Optimization Letters, 16, pages 1513-1529 (2022)

Vu Trung Hieu: Disconnectedness and unboundedness of the solution sets of monotone vector variational inequalities, Applicable Analysis, 100, pages 482-492 (2021)

Vu Trung Hieu: Solution maps of polynomial variational inequalities, Journal of Global Optimization, 77, pages 807–824 (2020)

Vu Trung Hieu: An application of the Tarski-Seidenberg theorem with quantifiers to vector variational inequalities, Minimax Theory and its Applications, 5, pages 019-031 (2020)

Vu Trung Hieu, Yimin Wei, Jen-Chih Yao: Notes on the optimization problems corresponding to polynomial complementarity problems, Journal of Optimization Theory and Applications, 184, pages 687-695 (2020)

Vu Trung Hieu: On the R0-tensors and the solution map of tensor complementarity problems, Journal of Optimization Theory and Applications, 181, pages 163-183(2019)

Vu Trung Hieu: On the numbers of connected components in the solution sets of polynomial vector variational inequalities, Journal of Optimization Theory and Applications, 181, pages 95-100(2019)

Vu Trung Hieu:  Numbers of the connected components of the solution sets of monotone affine vector variational inequalities, Journal of Global Optimization, 73, pages 223-237(2019)