{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:07:47Z","timestamp":1778717267937,"version":"3.51.4"},"reference-count":68,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Prime Minister Research Fellowship","award":["PMRF ID-2703573"],"award-info":[{"award-number":["PMRF ID-2703573"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s11075-025-02177-8","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T04:52:02Z","timestamp":1753246322000},"page":"1265-1315","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An inexact proximal point method with quasi-distance for quasiconvex multiobjective optimization problems on Riemannian manifolds"],"prefix":"10.1007","volume":"102","author":[{"given":"Balendu Bhooshan","family":"Upadhyay","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subham","family":"Poddar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Orizon Pereira","family":"Ferreira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaopeng","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jen-Chih","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"2177_CR1","doi-asserted-by":"crossref","unstructured":"Apolin\u00e1rio, H.C.F., Papa Quiroz, E.A., Oliveira, P.R.: A scalarization proximal point method for quasiconvex multiobjective minimization. J. Global Optim. 64, 79\u201396 (2016)","DOI":"10.1007\/s10898-015-0367-3"},{"issue":"1","key":"2177_CR2","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1080\/02331934.2022.2094794","volume":"73","author":"S Azami","year":"2024","unstructured":"Azami, S., Barani, A., Oveisiha, M.: Inexact proximal point algorithm for quasiconvex optimization problems on Hadamard manifolds. Optimization 73(1), 89\u2013112 (2024)","journal-title":"Optimization"},{"key":"2177_CR3","doi-asserted-by":"crossref","unstructured":"Bento, G.C., Bitar, S.D.B., Cruz Neto, J.X., Soubeyran, A., Oliveira Souza, J.C.: A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems. Comput. Optim. Appl. 75, 263\u2013290 (2020)","DOI":"10.1007\/s10589-019-00139-0"},{"key":"2177_CR4","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10957-018-1330-5","volume":"179","author":"GC Bento","year":"2018","unstructured":"Bento, G.C., Cruz Neto, J.X., Meireles, L.: Proximal point method for locally Lipschitz function in multiobjective optimization of Hadamard manifolds. J. Optim. Theory Appl. 179, 37\u201352 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"2177_CR5","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s11228-014-0279-2","volume":"22","author":"GC Bento","year":"2014","unstructured":"Bento, G.C., Cruz Neto, J.X., Soubeyran, A.: A proximal point-type method for multicriteria optimization. Set-Valued Var. Anal. 22, 557\u2013573 (2014)","journal-title":"Set-Valued Var. Anal."},{"key":"2177_CR6","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1016\/j.ejor.2014.01.002","volume":"235","author":"GC Bento","year":"2014","unstructured":"Bento, G.C., Cruz Neto, J.X., Oliveira, P.R., Soubeyran, A.: The self-regulation problem as an inexact steepest descent method for multicriteria optimization. European J. Oper. Res. 235, 494\u2013502 (2014)","journal-title":"European J. Oper. Res."},{"issue":"1","key":"2177_CR7","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.orl.2017.10.017","volume":"46","author":"GC Bento","year":"2018","unstructured":"Bento, G.C., Ferreira, O.P., Pereira, Y.R.: Proximal point method for vector optimization on Hadamard manifolds. Oper. Res. Lett. 46(1), 13\u201318 (2018)","journal-title":"Oper. Res. Lett."},{"issue":"2","key":"2177_CR8","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.na.2010.03.057","volume":"73","author":"GC Bento","year":"2010","unstructured":"Bento, G.C., Ferreira, O.P., Oliveira, P.R.: Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds. Nonlinear Anal. 73(2), 564\u2013572 (2010)","journal-title":"Nonlinear Anal."},{"issue":"4","key":"2177_CR9","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1137\/S1052623403429093","volume":"15","author":"H Bonnel","year":"2005","unstructured":"Bonnel, H., Iusem, A.N., Svaiter, B.F.: Proximal methods in vector optimization. SIAM J. Optim. 15(4), 953\u2013970 (2005)","journal-title":"SIAM J. Optim."},{"key":"2177_CR10","first-page":"553","volume":"20","author":"R Bergmann","year":"2019","unstructured":"Bergmann, R., Laus, F., Persch, J., Steidl, G.: Recent advances in denoising of manifold-valued images. Handb. Numer. Anal. 20, 553\u2013578 (2019)","journal-title":"Handb. Numer. Anal."},{"key":"2177_CR11","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/BF02761171","volume":"29","author":"H Br\u00e9zis","year":"1978","unstructured":"Br\u00e9zis, H., Lions, P.L.: Produits infinis de r\u00e9solvantes. Israel J. Math. 29, 329\u2013345 (1978)","journal-title":"Israel J. Math."},{"key":"2177_CR12","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/978-3-030-31351-7_22","volume-title":"Handbook of Variational Methods for Nonlinear Geometric Data","author":"M Baust","year":"2020","unstructured":"Baust, M., Weinmann, A.: Manifold-valued data in medical imaging applications. In: Grohs, P., Holler, M., Weinmann, A. (eds.) Handbook of Variational Methods for Nonlinear Geometric Data, pp. 613\u2013647. Springer, Cham (2020)"},{"issue":"1","key":"2177_CR13","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1137\/S1052623495286302","volume":"8","author":"RS Burachik","year":"1998","unstructured":"Burachik, R.S., Iusem, A.N.: A generalized proximal point algorithm for the variational inequality problem in a Hilbert space. SIAM J. Optim. 8(1), 197\u2013216 (1998)","journal-title":"SIAM J. Optim."},{"issue":"5","key":"2177_CR14","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1137\/S0363012998339745","volume":"39","author":"RS Burachik","year":"2001","unstructured":"Burachik, R.S., Scheimberg, S.: A proximal point algorithm for the variational inequality problem in Banach space. SIAM J. Control Optim. 39(5), 1633\u20131649 (2001)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"2177_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2006.09.070","volume":"183","author":"LC Ceng","year":"2007","unstructured":"Ceng, L.C., Yao, J.C.: Approximate proximal methods in vector optimization. European J. Oper. Res. 183(1), 1\u201319 (2007)","journal-title":"European J. Oper. Res."},{"key":"2177_CR16","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)"},{"key":"2177_CR17","doi-asserted-by":"crossref","unstructured":"do Carmo, M.P.: Riemannian Geometry. Birkh\u00e4user, Basel (1992)","DOI":"10.1007\/978-1-4757-2201-7"},{"key":"2177_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-2151-2","volume-title":"Facility Location: Concepts","author":"RZ Farahani","year":"2009","unstructured":"Farahani, R.Z., Hekmatfar, M.: Facility Location: Concepts. Springer, Verlag Berlin, Models, Algorithms and Case Studies (2009)"},{"key":"2177_CR19","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s10898-020-00889-w","volume":"77","author":"M Farrokhiniya","year":"2020","unstructured":"Farrokhiniya, M., Barani, A.: Limiting subdifferential calculus and perturbed distance function in Riemannian manifolds. J. Global Optim. 77, 661\u2013685 (2020)","journal-title":"J. Global Optim."},{"issue":"4","key":"2177_CR20","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1137\/18M1180633","volume":"29","author":"OP Ferreira","year":"2019","unstructured":"Ferreira, O.P., Louzeiro, M.S., Prudente, L.: Gradient method for optimization on Riemannian manifolds with lower bounded curvature. SIAM J. Optim. 29(4), 2517\u20132541 (2019)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2177_CR21","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1080\/02331930290019413","volume":"51","author":"OP Ferreira","year":"2002","unstructured":"Ferreira, O.P., Oliveira, P.R.: Proximal point algorithm on Riemannian manifolds. Optimization 51(2), 257\u2013270 (2002)","journal-title":"Optimization"},{"issue":"2","key":"2177_CR22","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1137\/08071692X","volume":"20","author":"J Fliege","year":"2009","unstructured":"Fliege, J., Gra\u00f1a Drummond, L.M., Svaiter, B.F.: Newton\u2019s method for multiobjective optimization. SIAM J. Optim. 20(2), 602\u2013626 (2009)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2177_CR23","first-page":"1","volume":"20","author":"A Ghosh","year":"2023","unstructured":"Ghosh, A., Upadhyay, B.B., Stancu-Minasian, I.M.: Constraint qualifications for multiobjective programming problems on Hadamard manifolds. Aust. J. Math. Anal. Appl. 20(2), 1\u201317 (2023)","journal-title":"Aust. J. Math. Anal. Appl."},{"key":"2177_CR24","doi-asserted-by":"publisher","first-page":"3649","DOI":"10.3390\/math11173649","volume":"11","author":"A Ghosh","year":"2023","unstructured":"Ghosh, A., Upadhyay, B.B., Stancu-Minasian, I.M.: Pareto efficiency criteria and duality for multiobjective fractional programming problems with equilibrium constraints on Hadamard manifolds. Mathematics 11, 3649 (2023)","journal-title":"Mathematics"},{"key":"2177_CR25","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1137\/0329022","volume":"29","author":"O G\u00fcler","year":"1991","unstructured":"G\u00fcler, O.: On the convergence of the proximal point algorithm for convex minimization. SIAM J. Control Optim. 29, 403\u2013419 (1991)","journal-title":"SIAM J. Control Optim."},{"issue":"12","key":"2177_CR26","doi-asserted-by":"publisher","first-page":"3884","DOI":"10.1016\/j.na.2011.02.023","volume":"74","author":"S Hosseini","year":"2011","unstructured":"Hosseini, S., Pouryayevali, M.R.: Generalized gradients and characterization of epi-Lipschitz sets in Riemannian manifolds. Nonlinear Anal. 74(12), 3884\u20133895 (2011)","journal-title":"Nonlinear Anal."},{"key":"2177_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2022.105860","volume":"145","author":"Z Hu","year":"2022","unstructured":"Hu, Z., Wang, L., Qin, J., Lev, B., Gan, L.: Optimization of facility location and size problem based on bi-level multi-objective programming. Comput. Oper. Res. 145, 105860 (2022)","journal-title":"Comput. Oper. Res."},{"key":"2177_CR28","doi-asserted-by":"publisher","first-page":"3687","DOI":"10.1090\/S0002-9947-07-04075-5","volume":"359","author":"YS Ledyaev","year":"2007","unstructured":"Ledyaev, Y.S., Zhu, Q.J.: Nonsmooth analysis on smooth manifolds. Trans. Amer. Math. Soc. 359, 3687\u20133732 (2007)","journal-title":"Trans. Amer. Math. Soc."},{"key":"2177_CR29","doi-asserted-by":"crossref","unstructured":"Lui, Y.M., Beveridge, J.R.: Grassmann registration manifolds for face recognition. In: Computer Vision\u2013ECCV 2008, Springer, pp. 44\u201357 (2008)","DOI":"10.1007\/978-3-540-88688-4_4"},{"issue":"3","key":"2177_CR30","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1007\/s40879-021-00469-6","volume":"7","author":"Y Lim","year":"2021","unstructured":"Lim, Y., Hiai, F., Lawson, J.: Nonhomogeneous Karcher equations with vector fields on positive definite matrices. European J. Math. 7(3), 1291\u20131328 (2021)","journal-title":"European J. Math."},{"key":"2177_CR31","doi-asserted-by":"crossref","unstructured":"Martinet, B.: Regularisation, d\u2019in\u00e9quations variationelles par approximations successive. Rev. Fr. Inform. Rech. Op\u00e9r. 4, 154\u2013159 (1970)","DOI":"10.1051\/m2an\/197004R301541"},{"key":"2177_CR32","volume-title":"Nonlinear Multiobjective Optimization","author":"K Miettinen","year":"1999","unstructured":"Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Norwell (1999)"},{"key":"2177_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-31246-3","volume-title":"Variational Analysis and Generalized Differentiation I: Basic Theory","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation I: Basic Theory. Springer, New York (2006)"},{"key":"2177_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-31246-3","volume-title":"Variational Analysis and Generalized Differentiation II: Applications","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation II: Applications. Springer, Berlin (2006)"},{"issue":"12","key":"2177_CR35","first-page":"1383","volume":"61","author":"FG Moreno","year":"2012","unstructured":"Moreno, F.G., Oliveira, P.R., Soubeyran, A.: A proximal algorithm with quasi distance. Application to habit\u2019s formation. Optimization 61(12), 1383\u20131403 (2012)","journal-title":"Application to habit\u2019s formation. Optimization"},{"key":"2177_CR36","doi-asserted-by":"crossref","unstructured":"Papa Quiroz, E.A., Apolin\u00e1rio, H.C.F., Villacorta, K.D., Oliveira, P.R.: A linear scalarization proximal point method for quasiconvex multiobjective minimization. J. Optim. Theory Appl. 183, 1028\u20131052 (2019)","DOI":"10.1007\/s10957-019-01582-z"},{"key":"2177_CR37","doi-asserted-by":"crossref","unstructured":"Papa Quiroz, E.A., Baygorrea, N., Maculan, N.: Convergence analysis of a generalized proximal algorithm for multiobjective quasiconvex minimization on Hadamard manifolds. Optimization 73(9), 2819\u20132844 (2024)","DOI":"10.1080\/02331934.2023.2234939"},{"key":"2177_CR38","doi-asserted-by":"publisher","first-page":"1445","DOI":"10.1007\/s10479-020-03622-8","volume":"316","author":"EA Papa Quiroz","year":"2022","unstructured":"Papa Quiroz, E.A., Cruzado, S.: An inexact scalarization proximal point method for multiobjective quasiconvex minimization. Ann. Oper. Res. 316, 1445\u20131470 (2022)","journal-title":"Ann. Oper. Res."},{"issue":"3","key":"2177_CR39","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1007\/s10957-020-01725-7","volume":"186","author":"EA Papa Quiroz","year":"2020","unstructured":"Papa Quiroz, E.A., Cusihuallpa, N.B., Maculan, N.: Inexact proximal point methods for multiobjective quasiconvex minimization on Hadamard manifolds. J. Optim. Theory Appl. 186(3), 879\u2013898 (2020)","journal-title":"J. Optim. Theory Appl."},{"key":"2177_CR40","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1016\/j.ejor.2015.05.041","volume":"246","author":"EA Papa Quiroz","year":"2015","unstructured":"Papa Quiroz, E.A., Mallma Ramirez, L., Oliveira, P.R.: An inexact proximal method for quasiconvex minimization. European J. Oper. Res. 246, 721\u2013729 (2015)","journal-title":"European J. Oper. Res."},{"key":"2177_CR41","doi-asserted-by":"publisher","first-page":"5924","DOI":"10.1016\/j.na.2012.06.005","volume":"75","author":"EA Papa Quiroz","year":"2012","unstructured":"Papa Quiroz, E.A., Oliveira, P.R.: Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds. Nonlinear Anal. 75, 5924\u20135932 (2012)","journal-title":"Nonlinear Anal."},{"issue":"1","key":"2177_CR42","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1051\/ro\/2017078","volume":"52","author":"EA Papa Quiroz","year":"2018","unstructured":"Papa Quiroz, E.A., Ramirez, L.M., Oliveira, P.R.: An inexact algorithm with proximal distances for variational inequalities. RAIRO Oper. Res. 52(1), 159\u2013176 (2018)","journal-title":"RAIRO Oper. Res."},{"issue":"4","key":"2177_CR43","doi-asserted-by":"publisher","first-page":"2301","DOI":"10.1051\/ro\/2023101","volume":"57","author":"EA Papa Quiroz","year":"2023","unstructured":"Papa Quiroz, E.A., Rocha, R.A., Oliveira, P., Greg\u00f3rio, R.: Proximal algorithm with quasi-distances for multiobjective quasiconvex minimization in Riemannian manifolds. RAIRO Oper. Res. 57(4), 2301\u20132314 (2023)","journal-title":"RAIRO Oper. Res."},{"issue":"7","key":"2177_CR44","doi-asserted-by":"publisher","first-page":"1570","DOI":"10.3390\/math11071570","volume":"11","author":"Z Peng","year":"2023","unstructured":"Peng, Z., Li, H., Zhao, D., Pan, C.: Reducing the dimensionality of SPD matrices with neural networks in BCI. Mathematics 11(7), 1570 (2023)","journal-title":"Mathematics"},{"issue":"1","key":"2177_CR45","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.apm.2010.06.009","volume":"35","author":"L Pourkarimi","year":"2011","unstructured":"Pourkarimi, L., Yaghoobi, M.A., Mashinchi, M.: Efficient curve fitting: An application of multiobjective programming. Appl. Math. Modell. 35(1), 346\u2013365 (2011)","journal-title":"Appl. Math. Modell."},{"key":"2177_CR46","volume-title":"Smooth Nonlinear Optimization in $$\\mathbb{R} ^n$$","author":"T Rapcs\u00e1k","year":"2013","unstructured":"Rapcs\u00e1k, T.: Smooth Nonlinear Optimization in $$\\mathbb{R} ^n$$. Springer, Berlin (2013)"},{"key":"2177_CR47","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1007\/s10957-016-1005-z","volume":"171","author":"RA Rocha","year":"2016","unstructured":"Rocha, R.A., Oliveira, P.R., Greg\u00f3rio, R.M., Souza, M.: A proximal point algorithm with quasi-distance in multi-objective optimization. J. Optim. Theory Appl. 171, 964\u2013979 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"5","key":"2177_CR48","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877\u2013898 (1976)","journal-title":"SIAM J. Control Optim."},{"key":"2177_CR49","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"1","key":"2177_CR50","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/S0022-247X(03)00285-3","volume":"283","author":"S Romaguera","year":"2003","unstructured":"Romaguera, S., Sanchis, M.: Applications of utility functions defined on quasi-metric spaces. J. Math. Anal. Appl. 283(1), 219\u2013235 (2003)","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"2177_CR51","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1287\/moor.25.2.214.12222","volume":"25","author":"MV Solodov","year":"2000","unstructured":"Solodov, M.V., Svaiter, B.F.: An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions. Math. Oper. Res. 25(2), 214\u2013230 (2000)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"2177_CR52","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/j.ejor.2009.03.045","volume":"201","author":"S Souza","year":"2010","unstructured":"Souza, S., Oliveira, P., Cruz Neto, J.X., Soubeyran, A.: A proximal point algorithm with separable Bregman distances for quasiconvex optimization over the nonnegative orthant. European J. Oper. Res. 201(2), 365\u2013376 (2010)","journal-title":"European J. Oper. Res."},{"key":"2177_CR53","first-page":"639","volume":"84","author":"S Treitl","year":"2014","unstructured":"Treitl, S., Jammernegg, W.: Facility location decisions with environmental considerations: a case study from the petrochemical industry. J. Bus. Econo. 84, 639\u2013664 (2014)","journal-title":"J. Bus. Econo."},{"key":"2177_CR54","volume-title":"Convex Functions and Optimization Methods on Riemannian Manifolds","author":"C Udri\u015fte","year":"2013","unstructured":"Udri\u015fte, C.: Convex Functions and Optimization Methods on Riemannian Manifolds. Springer, Berlin (2013)"},{"issue":"1","key":"2177_CR55","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10957-023-02207-2","volume":"199","author":"BB Upadhyay","year":"2023","unstructured":"Upadhyay, B.B., Ghosh, A.: On constraint qualifications for mathematical programming problems with vanishing constraints on Hadamard manifolds. J. Optim. Theory Appl. 199(1), 1\u201335 (2023)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"2177_CR56","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1007\/s10957-023-02301-5","volume":"200","author":"BB Upadhyay","year":"2023","unstructured":"Upadhyay, B.B., Ghosh, A., Trean\u021ba, S.: Constraint qualifications and optimality criteria for nonsmooth multiobjective programming problems on Hadamard manifolds. J. Optim. Theory Appl. 200(2), 794\u2013819 (2023)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"2177_CR57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2023.127785","volume":"531","author":"BB Upadhyay","year":"2023","unstructured":"Upadhyay, B.B., Ghosh, A., Trean\u021ba, S.: Optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints on Hadamard manifolds. J. Math. Anal. Appl. 531(1), 127785 (2023)","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"2177_CR58","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.3934\/jimo.2023138","volume":"20","author":"BB Upadhyay","year":"2024","unstructured":"Upadhyay, B.B., Pandey, R.K., Liao, S.: Newton\u2019s method for interval-valued multiobjective optimization problem. J. Ind. Manag. Optim. 20(4), 1633\u20131661 (2024)","journal-title":"J. Ind. Manag. Optim."},{"key":"2177_CR59","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115550","volume":"438","author":"BB Upadhyay","year":"2024","unstructured":"Upadhyay, B.B., Pandey, R.K., Pan, J., Zeng, S.: Quasi-Newton algorithms for solving interval-valued multiobjective optimization problems by using their certain equivalence. J. Comput. Appl. Math. 438, 115550 (2024)","journal-title":"J. Comput. Appl. Math."},{"key":"2177_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2024.109066","volume":"492","author":"BB Upadhyay","year":"2024","unstructured":"Upadhyay, B.B., Pandey, R.K., Zeng, S.: A generalization of generalized Hukuhara Newton\u2019s method for interval-valued multiobjective optimization problems. Fuzzy Sets Syst. 492, 109066 (2024)","journal-title":"Fuzzy Sets Syst."},{"key":"2177_CR61","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s10479-024-06461-z","volume":"345","author":"BB Upadhyay","year":"2025","unstructured":"Upadhyay, B.B., Poddar, S., Yao, J.C., Zhao, X.: Inexact proximal point method with a Bregman regularization for quasiconvex multiobjective optimization problems via limiting subdifferentials. Ann. Oper. Res. 345, 417\u2013466 (2025)","journal-title":"Ann. Oper. Res."},{"issue":"12","key":"2177_CR62","doi-asserted-by":"publisher","first-page":"3081","DOI":"10.1080\/02331934.2022.2088369","volume":"72","author":"BB Upadhyay","year":"2022","unstructured":"Upadhyay, B.B., Trean\u0163\u0103, S., Mishra, P.: On Minty variational principle for nonsmooth multiobjective optimization problems on Hadamard manifolds. Optimization 72(12), 3081\u20133100 (2022)","journal-title":"Optimization"},{"issue":"4","key":"2177_CR63","doi-asserted-by":"publisher","first-page":"2696","DOI":"10.1137\/15M1051257","volume":"26","author":"J Wang","year":"2016","unstructured":"Wang, J., Li, C., Lopez, G., Yao, J.C.: Proximal point algorithms on Hadamard manifolds: linear convergence and finite termination. SIAM J. Optim. 26(4), 2696\u20132729 (2016)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2177_CR64","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10957-023-02235-y","volume":"198","author":"XM Wang","year":"2023","unstructured":"Wang, X.M., Wang, J.H., Li, C.: Convergence of inexact steepest descent algorithm for multiobjective optimizations on Riemannian manifolds without curvature constraints. J. Optim. Theory Appl. 198(1), 187\u2013214 (2023)","journal-title":"J. Optim. Theory Appl."},{"key":"2177_CR65","doi-asserted-by":"crossref","unstructured":"Watterson, M., Liu, S., Sun, K., Smith, T., Kumar, V.: Trajectory optimization on manifolds with applications to $$SO(3)$$ and $$\\mathbb{R}^{3} \\times S^{2}$$. In: Proceedings of Robotics: Science and Systems. Pittsburgh, PA, USA, 2018, pp. 1-9 (2018)","DOI":"10.15607\/RSS.2018.XIV.023"},{"issue":"3","key":"2177_CR66","doi-asserted-by":"publisher","first-page":"1523","DOI":"10.1137\/20M1360748","volume":"32","author":"L Yang","year":"2022","unstructured":"Yang, L., Toh, K.C.: Bregman proximal point algorithm revisited: a new inexact version and its inertial variant. SIAM J. Optim. 32(3), 1523\u20131554 (2022)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"2177_CR67","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11117-024-01057-0","volume":"28","author":"X Zhao","year":"2024","unstructured":"Zhao, X., Ji, H., Ghosh, D., Yao, J.C.: An inexact proximal point method with quasi-distance for quasiconvex multiobjective optimization. Positivity 28(3), 1\u201319 (2024)","journal-title":"Positivity"},{"issue":"5","key":"2177_CR68","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s40314-024-02828-x","volume":"43","author":"X Zhao","year":"2024","unstructured":"Zhao, X., Qi, M., Jolaoso, L.O., Shehu, Y., Yao, J.C., Yao, Y.: An inexact proximal point method for quasiconvex multiobjective optimization. Comput. Appl. Math. 43(5), 309 (2024)","journal-title":"Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02177-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-025-02177-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02177-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T23:11:56Z","timestamp":1778713916000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-025-02177-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,23]]},"references-count":68,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["2177"],"URL":"https:\/\/doi.org\/10.1007\/s11075-025-02177-8","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,23]]},"assertion":[{"value":"28 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors affirm that there are no actual or potential conflicts of interest associated with this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interests"}},{"value":"All the authors have read and endorsed the final manuscript.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}