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All issues Volume 60 / No 3 (May-June 2026) RAIRO-Oper. Res., 60 3 (2026) 1621-1643 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 60, Number 3, May-June 2026
Page(s) 1621 - 1643
DOI https://doi.org/10.1051/ro/2026036
Published online 19 June 2026
  • A. Barani, Generalized monotonicity and convexity for locally Lipschitz functions on Hadamard manifolds. Diff. Geom. Dyn. Syst. 15 (2013) 26–37. [Google Scholar]
  • G.C. Bento, O.P. Ferreira and P.R. Oliveira, Proximal point method for a special class of nonconvex functions on Hadamard manifolds. Optimization. 64 (2015) 289–319. [Google Scholar]
  • R. Bhatia, Positive Definite Matrices, in Princeton Series in Applied Mathematics. Princeton University Press, New Jersey (2007). [Google Scholar]
  • J.V. Burke and M.C. Ferris, Characterization of solution sets of convex programs. Oper. Res. Lett. 10 (1991) 57–60. [Google Scholar]
  • S.L. Chen and C. Fang, Vector variational inequality with pseudoconvexity on Hadamard manifolds. Optimization. 65 (2016) 2067–2080. [CrossRef] [MathSciNet] [Google Scholar]
  • S.L. Chen and N..J. Huang, Vector variational inequalities and vector optimization problems on Hadamard manifolds. Optim. Lett. 10 (2016) 753–767. [Google Scholar]
  • H. Chen, X. Li and Q. Sun, Statistical analysis of Karcher means for random restricted PSD matrices, in Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS), Vol. 206. Valencia, Spain (2023). [Google Scholar]
  • K.L. Chew and E.U. Choo, Pseudolinearity and efficiency. Math. Program. 28 (1984) 226–239. [Google Scholar]
  • N. Dinh, V. Jeyakumar and G.M. Lee, Lagrange multiplier characterizations of solution sets of constrained pseudo- linear optimization problems. Optimization. 55 (2006) 241–250. [Google Scholar]
  • M. Farrokhiniya and A. Barani, Limiting subdifferential calculus and perturbed distance function in Riemannian manifolds. J. Global Optim. 77 (2020) 661–685. [Google Scholar]
  • S. Hosseini and M.R. Pouryayevali, Generalized gradients and characterization of epi-Lipschitz sets in Riemannian manifolds. Nonlinear Anal. 74 (2011) 3884–3895. [Google Scholar]
  • A. Jayswal, B. Kumari and I. Ahmad, Vector variational inequalities on Riemannian manifolds with approximate geodesic star-shaped functions. Rend. Circ. Mat. Palermo (2) 72 (2021) 157–167. [Google Scholar]
  • V. Jeyakumar and X.Q. Yang, On characterizing the solution sets of pseudolinear programs. J. Optim. Theory Appl. 87 (1995) 745–755. [Google Scholar]
  • R.N. Kaul, V. Lyall and S. Kaur, Semilocal pseudolinearity and efficiency. Eur. J. Oper. Res. 36 (1988) 402–409. [Google Scholar]
  • S. Kruk and H. Wolkowicz, Pseudolinear programming. SIAM Rev. 41 (1999) 795–805. [Google Scholar]
  • S. Komlósi, First and second order characterizations of pseudolinear functions. Eur. J. Oper. Res. 67 (1993) 278–286. [Google Scholar]
  • K.O. Kortanek and J.P. Evans, Pseudoconcave programming and Lagrange regularity. Oper. Res. 15 (1967) 882–892. [Google Scholar]
  • C.S. Lalitha and M. Mehta, Characterization of the solution sets of pseudolinear programs and pseudoaffine varia- tional inequality problems. J. Nonlinear Convex Anal. 8 (2007) 87–98. [Google Scholar]
  • Y.S. Ledyaev and Q.J. Zhu, Nonsmooth analysis on smooth manifolds. Trans. Amer. Math. Soc. 359 (2007) 3687–3732. [Google Scholar]
  • J. Lawson and Y. Lim, Karcher means and Karcher equations of positive definite operators. Trans. Amer. Math. Soc. 1 (2014) 1–22. [Google Scholar]
  • C. Li, G. López and V. Martín-Márquez, Monotone vector fields and the proximal point algorithm on Hadamard manifolds. J. Lond. Math. Soc. 79 (2009) 663–683. [Google Scholar]
  • X.B. Li, Y.B. Xiao and N.J. Huang, Some characterizations for the solution sets of pseudoaffine programs, convex programs and variational inequalities on Hadamard manifolds. Pac. J. Optim. 12 (2016) 307–325. [Google Scholar]
  • Q.H. Lu and D.L. Zhu, Some characterizations of locally Lipschitz pseudolinear functions. Math. Appl. 18 (2005) 272–278. [Google Scholar]
  • O.L. Mangasarian, Nonlinear Programming. McGraw-Hill (1969). [Google Scholar]
  • O.L. Mangasarian, A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7 (1998) 21–26. [Google Scholar]
  • S.K. Mishra and B.B. Upadhyay, Efficiency and duality in nonsmooth multiobjective fractional programming involv- ing -pseudolinear functions. Yugosl. J. Oper. Res. 22 (2012) 3–18. [Google Scholar]
  • S.K. Mishra and B.B. Upadhyay, Duality in non-smooth multi-objective programming involving n-pseudolinear functions. ISIAM 3 (2012) 152–161. [Google Scholar]
  • S.K. Mishra and B.B. Upadhyay, Nonsmooth minimax fractional programming involving 17-pseudolinear functions. Optimization. 63 (2014) 775–788. [Google Scholar]
  • S.K. Mishra and B.B. Upadhyay, Pseudolinear Functions and Optimization. CRC Press (2015). [Google Scholar]
  • S.K. Mishra, B.B. Upadhyay and L.T. An, Lagrange multiplier characterizations of solution sets of constrained nonsmooth pseudolinear optimization problems. J. Optim. Theory Appl. 160 (2014) 763–777. [Google Scholar]
  • S.Z. Németh, Five kinds of monotone vector fields. Pure Math. Appl. (1999) 417–428. [Google Scholar]
  • S.Z. Németh, Variational inequalities on Hadamard manifolds. Nonlinear Anal. 52 (2003) 1491–1498. [Google Scholar]
  • A.M. Neuman, Y. Xie and Q. Sun, Restricted Riemannian geometry for positive semidefinite matrices. Linear Algebra Appl. 665 (2023) 153–195. [Google Scholar]
  • T. Rapesák, On pseudolinear functions. Eur. J. Oper. Res. 50 (2011) 353–360. [Google Scholar]
  • T. Rapscák, Smooth Nonlinear Optimization in ℝn. Kluwer Academic Publishers (1997). [Google Scholar]
  • T. Sakai, Riemannian Geometry. American Mathematical Society (1996). [Google Scholar]
  • G.J. Tang and N.J. Huang, Korpelevich's methods for variational inequality problems on Hadamard manifolds. J. Global Optim. 54 (2012) 493–509. [Google Scholar]
  • W. Thämelt, Directional derivatives and generalized gradients on manifolds. Optimization. 25 (1992) 97–115. [Google Scholar]
  • N. Thorstensen, F. Ségonne and R. Keriven, Pre-image as Karcher mean using diffusion maps: application to shape and image denoising, Vol. 5567 in Proceedings of SSVM (2009) 721–732. [Google Scholar]
  • C. Udriște, Convex Functions and Optimization Methods on Riemannian Manifolds. Kluwer Academic Publishers (1994). [Google Scholar]
  • B.B. Upadhyay, A. Ghosh, P. Mishra and S. Treantɜ˘a, Optimality conditions and duality for multiobjective semiinfinite programming problems on Hadamard manifolds using generalized geodesic convexity. RAIRO Oper. Res. 56 (2022) 2037–2065. [Google Scholar]
  • B.B. Upadhyay, S. Minasian, P. Mishra and R.N. Mohapatra, On generalized vector variational inequalities and nonsmooth vector optimization problems on Hadamard manifolds involving geodesic approximate convexity. Adv. Nonlinear Var. Inequal. 25 (2022) 1–25. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh and S. Treantɜ˘a, Optimality conditions and duality for nonsmooth multiobjective semiinfinite programming problems on Hadamard manifolds. Bull. Iran. Math. Soc. 49 (2023) 1–36. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh and S. Treantɜ˘a, Optimality conditions and duality for nonsmooth multiobjective semiinfinite programming problems with vanishing constraints on Hadamard manifolds. J. Math. Anal. Appl. 531 (2023) 127785. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh, On constraint qualifications for mathematical programming problems with vanishing constraints on Hadamard manifolds. J. Optim. Theory Appl. 199 (2023) 1–35. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh and S. Treantɜ˘a, Constraint qualifications and optimality criteria for nonsmooth multiobjective programming problems on Hadamard manifolds. J. Optim. Theory Appl. 200 (2024) 794–819. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh and I.M. Stancu-Minasian, Second-order optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds. Asia-Pac. J. Oper. Res. 41 (2024). [Google Scholar]
  • B.B. Upadhyay, A. Ghosh and S. Treantɜ˘a, Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds. J. Global Optim. 89 (2024) 723–744. [Google Scholar]
  • B.B. Upadhyay, S.K. Mishra and P. Maréchal (eds.), Convex Optimization-Theory, Algorithms and Applications. Springer, Berlin (2025). [Google Scholar]
  • X. Yuan, W. Huang, P.-A. Absil and K.A. Gallivan, Computing the matrix geometric mean: Riemannian vs Euclidean conditioning, implementation techniques, and a Riemannian BFGS method. Numer. Linear Algebra Appl. 27 (2020). [Google Scholar]
  • K.Q. Zhao and L.P. Tang, On characterizing solution set of non-differentiable η-pseudolinear extremum problem. Optimization. 61 (2012) 239–249. [Google Scholar]

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