Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds

This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework o...

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Vydané v:	Journal of optimization theory and applications Ročník 200; číslo 2; s. 794 - 819
Hlavní autori:	Upadhyay, Balendu Bhooshan, Ghosh, Arnav, Treanţă, Savin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.02.2024 Springer Nature B.V
Predmet:	Applications of Mathematics Applied mathematics Banach spaces Calculus of Variations and Optimal Control; Optimization Constraints Convex analysis Engineering Euclidean space Geometry Manifolds Mathematical programming Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimality criteria Optimization Pareto optimum Qualifications Theory of Computation Optimality conditions 90C30 90C46 Constraint qualifications Hadamard manifolds 90C29 90C48 Mathematical programming
ISSN:	0022-3239, 1573-2878
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Abstract	This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.
AbstractList	This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.
Author	Upadhyay, Balendu Bhooshan Treanţă, Savin Ghosh, Arnav
Author_xml	– sequence: 1 givenname: Balendu Bhooshan surname: Upadhyay fullname: Upadhyay, Balendu Bhooshan organization: Department of Mathematics, Indian Institute of Technology Patna – sequence: 2 givenname: Arnav surname: Ghosh fullname: Ghosh, Arnav organization: Department of Mathematics, Indian Institute of Technology Patna – sequence: 3 givenname: Savin orcidid: 0000-0001-8209-3869 surname: Treanţă fullname: Treanţă, Savin email: savin.treanta@upb.ro organization: Department of Applied Mathematics, University Politehnica of Bucharest, Academy of Romanian Scientists, 54 Splaiul Independentei, Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest
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Cites_doi	10.1137/15M101988X 10.1051/ro:2004023 10.1016/B978-0-12-814725-2.00010-8 10.1515/9783110361629 10.3390/math10193516 10.1007/s10957-022-02107-x 10.1007/s41980-021-00646-z 10.1016/j.na.2011.02.023 10.1007/978-1-4419-9640-4_11 10.1080/02331934.2012.679939 10.1007/s10957-023-02207-2 10.2298/FIL1703781G 10.1016/j.jmaa.2004.08.036 10.1142/S0217595923500197 10.1007/s10898-020-00889-w 10.1016/j.na.2006.04.019 10.1051/ro/2022098 10.1023/B:MACH.0000033120.25363.1e 10.1137/18M1181602 10.1515/9781400830244 10.1525/9780520411586-036 10.1023/A:1004607615343 10.1023/A:1021794505701 10.1016/S0022-247X(03)00535-3 10.1007/s10107-019-01380-5 10.1051/cocv/2011102 10.1007/s10957-019-01539-2 10.1090/S0002-9947-07-04075-5 10.1137/1.9781611971255 10.3390/sym11081037 10.1007/978-3-662-47044-2_6 10.1007/BF02193099 10.1007/s41980-023-00791-7 10.1080/02331939608844241 10.1007/s10444-015-9426-z 10.1007/BF02207776 10.1137/18M1180633 10.1080/02331930410001661505 10.1007/s10957-020-01725-7 10.1016/j.jmaa.2005.08.049 10.1016/j.jmaa.2007.10.010 10.1007/s40879-021-00469-6 10.1007/s11750-008-0058-z 10.1080/02331934.2016.1235161 10.11650/tjm/180501 10.1016/j.jfa.2004.10.008 10.1080/02331939508844093 10.1080/02331934.2022.2088369 10.1007/978-3-642-22300-6_33 10.1023/B:JOTA.0000037607.48762.45
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References	UpadhyayBBGhoshAStancu-MinasianIMSecond-order optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifoldsAsia Pac. J. Oper. Res.202310.1142/S0217595923500197 YangWHZhangL-HSongROptimality conditions for the nonlinear programming problems on Riemannian manifoldsPac. J. Optim.2014104154343235056 TungLTTamDHOptimality conditions and duality for multiobjective semi-infinite programming on Hadamard manifoldsBull. Iran. Math. Soc.202248219122194487705 PennecXPennecXSommerSFletcherTManifold-valued image processing with SPD matricesRiemannian Geometric Statistics in Medical Image Analysis2020AmsterdamElsevier75134 Ruiz-GarzónGOsuna-GómezRRuiz-ZapateroJNecessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifoldsSymmetry2019111037 AbsilP-AMahonyRSepulchreROptimization Algorithms on Matrix Manifolds2008PrincetonPrinceton University Press LiXFConstraint qualifications in nonsmooth multiobjective optimizationJ. Optim. Theory Appl.20001063733981788930 PredaVChiescuIOn constraint qualification in multiobjective optimization problems: semidifferentiable caseJ. Optim. Theory Appl.19991004174331673442 FerreiraOPLouzeiroMSPrudenteLGradient method for optimization on Riemannian manifolds with lower bounded curvatureSIAM J. Optim.2019294251725414018420 Papa QuirozEABaygorrea CusihuallpaNMaculanNInexact proximal point methods for multiobjective quasiconvex minimization on Hadamard manifoldsJ. Optim. Theory Appl.202018638798984142932 Upadhyay, B.B., Ghosh, A., Treanţă, S.: Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds. Submitted in J. Glob. Optim. (2022) MaedaTConstraint qualifications in multiobjective optimization problems: differentiable caseJ. Optim. Theory Appl.19948034835001265172 MishraSKLagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programmingOptimization1996382931051410216 UdrişteCConvex Functions and Optimization Methods on Riemannian Manifolds2013BerlinSpringer Mangasarian, O.L.: Nonlinear Programming. SIAM Classics in Applied Mathematics, vol. 10. McGraw-Hill, New York (1969). Reprint Philadelphia (1994) DuttaJChandraSConvexificators, generalized convexity and vector optimizationOptimization20045377942040636 FarrokhiniyaMBaraniALimiting subdifferential calculus and perturbed distance function in Riemannian manifoldsJ. Glob. Optim.2020776616854102430 Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. Berkeley (1950) MishraSKWangSYLaiKKOptimality and duality for multiple objective optimization under generalized type I univexityJ. Math. Anal. Appl.20053033153262113884 LimYHiaiFLawsonJNonhomogeneous Karcher equations with vector fields on positive definite matricesEur. J. Math.202173129113284289869 Ruiz-GarzónGOsuna-GómezRRufián-LizanaAHernández-JiménezBOptimality and duality on Riemannian manifoldsTaiwan J. Math.201822124512593859374 BergmannRHerzogRIntrinsic formulation of KKT conditions and constraint qualifications on smooth manifoldsSIAM J. Optim.2019294242324444014790 GolestaniMNobakhtianSNonsmooth multiobjective programming and constraint qualificationsOptimization20136267837953060962 Fletcher, P.T., Moeller, J., Phillips, J.M., Venkatasubramanian, S.: Horoball hulls and extents in positive definite space. In: Algorithms and Data Structures, pp. 386–398 (2011) BaraniAGeneralized monotonicity and convexity for locally Lipschitz functions on Hadamard manifoldsDiffer. Geom. Dyn. Syst.20131526373073069 BacákMBergmannRSteidlGWeinmannAA second order nonsmooth variational model for restoring manifold-valued imagesSIAM J. Sci. Comput.201638A567A5973463052 RapcsákTSmooth Nonlinear Optimization in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R} }^n$$\end{document}2013BerlinSpringer ChenS-IHuangN-JO’ReganDGeodesic B-preinvex functions and multiobjective optimization problems on Riemannian manifoldsJ. Appl. Math.20142014Art. ID 524698, 12 pp.3191123 SteinOOn constraint qualifications in nonsmooth optimizationJ. Optim. Theory Appl.20041216476712084347 BergmannRHerzogROrtiz LópezJSchielaAFirst-and second-order analysis for optimization problems with manifold-valued constraintsJ. Optim. Theory Appl.202219525966234504979 FerreiraOPProximal subgradient and a characterization of Lipschitz function on Riemannian manifoldsJ. Math. Anal. Appl.20063135875972183321 HamdiAMishraSKMishraSKDecomposition methods based on augmented Lagrangians: a surveyTopics in Nonconvex Optimization2011New YorkSpringer175203 Papa QuirozEAOliveiraPRFull convergence of the proximal point method for quasiconvex functions on Hadamard manifoldsESAIM Control Optim. Cal. Var.20121824835002954635 MishraSKSinghVLahaVMohapatraRNXuHWangSWuSYOn constraint qualifications for multiobjective optimization problems with vanishing constraintsOptimization Methods, Theory and Applications2015HeidelbergSpringer95135 JouraniAConstraint qualifications and Lagrange multipliers in nondifferentiable programming problemsJ. Optim. Theory Appl.1994815335481281737 GiorgiGJimenezBNovoVStrong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problemsTop20091722883042576424 GuptaRSrivastavaMConstraint qualifications in nonsmooth multiobjective optimization problemFilomat20173137817973628821 UpadhyayBBGhoshATreanţăSOptimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems on Hadamard manifoldsBull. Iran. Math. Soc.20234945460551410.1007/s41980-023-00791-7 ChenS-IFangC-JVector variational inequality with pseudoconvexity on Hadamard manifoldsOptimization201665206720803564905 GiorgiGJimenezBNovoVOn constraint qualification in directionally differentiable multiobjective optimization problemsRAIRO-Oper. Res.2004382552742091756 KarkhaneeiMMMahdavi-AmiriNNonconvex weak sharp minima on Riemannian manifoldsJ. Optim. Theory Appl.2019183851043989298 HosseiniSPouryayevaliMRGeneralized gradients and characterization of epi-Lipschitz sets in Riemannian manifoldsNonlinear Anal.201174388438952802974 AzagraDFerreraJLópez-MesasFNonsmooth analysis and Hamilton–Jacobi equations on Riemannian manifoldsJ. Funct. Anal.20052203043612119282 BoumalNMishraBAbsilP-ASepulchreRManopt, a Matlab toolbox for optimization on manifoldsJ. Mach. Learn. Res.201415114551459 BelkinMNiyogiPSemi-supervised learning on Riemannian manifoldsMach. Learn.2004561209239 UpadhyayBBGhoshAMishraPTreanţăSOptimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds using generalized geodesic convexityRAIRO Oper. Res.2022564203720654450251 BačákMConvex Analysis and Optimization in Hadamard Spaces2014BerlinDe Gruyter GrohsPHosseiniSϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-subgradient algorithms for locally Lipschitz functions on Riemannian manifoldsAdv. Comput. Math.20164223333603477792 BaraniAOn pseudoconvex functions in Riemannian manifoldsJ. Finsler Geom. Appl.20212214224596892 LedyaevYSZhuQJNonsmooth analysis on smooth manifoldsTrans. Am. Math. Soc.2007359368737322302512 MishraSKMukherjeeRNGeneralized convex composite multiobjective nonsmooth programming and conditional proper efficiencyOptimization19953453661337615 ChryssochoosIVinterRBOptimal control problems on manifolds: a dynamic programming approachJ. Math. Anal. Appl.20032871181402010261 UpadhyayBBGhoshAOn constraint qualifications for mathematical programming problems with vanishing constraints on Hadamard manifoldsJ. Optim. Theory Appl.2023465105810.1007/s10957-023-02207-2 Papa QuirozEAQuispeEMOliveiraPRSteepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifoldsJ. Math. Anal. Appl.200934114674772394099 UpadhyayBBTreanţăSMishraPOn Minty variational principle for nonsmooth multiobjective optimization problems on Hadamard manifoldsOptimization202210.1080/02331934.2022.2088369 AzagraDFerreraJApplications of proximal calculus to fixed point theory on Riemannian manifoldsNonlinear Anal.2007671541742313886 Papa QuirozEAOliveiraPRProximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifoldsJ. Convex Anal.20091649692531192 TreanSUpadhyayBBGhoshANonlaoponKOptimality conditions for multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifoldsMathematics2022103516 MehlitzPStationarity conditions and constraint qualifications for mathematical programs with switching constraintsMath. 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References_xml	– reference: KarkhaneeiMMMahdavi-AmiriNNonconvex weak sharp minima on Riemannian manifoldsJ. Optim. Theory Appl.2019183851043989298 – reference: BaraniAGeneralized monotonicity and convexity for locally Lipschitz functions on Hadamard manifoldsDiffer. Geom. Dyn. Syst.20131526373073069 – reference: LiXFConstraint qualifications in nonsmooth multiobjective optimizationJ. Optim. Theory Appl.20001063733981788930 – reference: DuttaJChandraSConvexificators, generalized convexity and vector optimizationOptimization20045377942040636 – reference: Ruiz-GarzónGOsuna-GómezRRuiz-ZapateroJNecessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifoldsSymmetry2019111037 – reference: FerreiraOPProximal subgradient and a characterization of Lipschitz function on Riemannian manifoldsJ. Math. Anal. Appl.20063135875972183321 – reference: Mangasarian, O.L.: Nonlinear Programming. SIAM Classics in Applied Mathematics, vol. 10. McGraw-Hill, New York (1969). Reprint Philadelphia (1994) – reference: FarrokhiniyaMBaraniALimiting subdifferential calculus and perturbed distance function in Riemannian manifoldsJ. Glob. Optim.2020776616854102430 – reference: GiorgiGJimenezBNovoVStrong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problemsTop20091722883042576424 – reference: BacákMBergmannRSteidlGWeinmannAA second order nonsmooth variational model for restoring manifold-valued imagesSIAM J. Sci. Comput.201638A567A5973463052 – reference: ChenS-IHuangN-JO’ReganDGeodesic B-preinvex functions and multiobjective optimization problems on Riemannian manifoldsJ. Appl. Math.20142014Art. ID 524698, 12 pp.3191123 – reference: UpadhyayBBGhoshAStancu-MinasianIMSecond-order optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifoldsAsia Pac. J. Oper. Res.202310.1142/S0217595923500197 – reference: YangWHZhangL-HSongROptimality conditions for the nonlinear programming problems on Riemannian manifoldsPac. J. Optim.2014104154343235056 – reference: MehlitzPStationarity conditions and constraint qualifications for mathematical programs with switching constraintsMath. Program.202018111491864095903 – reference: GiorgiGJimenezBNovoVOn constraint qualification in directionally differentiable multiobjective optimization problemsRAIRO-Oper. Res.2004382552742091756 – reference: LimYHiaiFLawsonJNonhomogeneous Karcher equations with vector fields on positive definite matricesEur. J. Math.202173129113284289869 – reference: Papa QuirozEAOliveiraPRProximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifoldsJ. Convex Anal.20091649692531192 – reference: Papa QuirozEAOliveiraPRFull convergence of the proximal point method for quasiconvex functions on Hadamard manifoldsESAIM Control Optim. Cal. Var.20121824835002954635 – reference: AzagraDFerreraJLópez-MesasFNonsmooth analysis and Hamilton–Jacobi equations on Riemannian manifoldsJ. Funct. Anal.20052203043612119282 – reference: BergmannRHerzogROrtiz LópezJSchielaAFirst-and second-order analysis for optimization problems with manifold-valued constraintsJ. Optim. Theory Appl.202219525966234504979 – reference: UpadhyayBBGhoshAMishraPTreanţăSOptimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds using generalized geodesic convexityRAIRO Oper. Res.2022564203720654450251 – reference: AzagraDFerreraJApplications of proximal calculus to fixed point theory on Riemannian manifoldsNonlinear Anal.2007671541742313886 – reference: BačákMConvex Analysis and Optimization in Hadamard Spaces2014BerlinDe Gruyter – reference: GuptaRSrivastavaMConstraint qualifications in nonsmooth multiobjective optimization problemFilomat20173137817973628821 – reference: HosseiniSPouryayevaliMRGeneralized gradients and characterization of epi-Lipschitz sets in Riemannian manifoldsNonlinear Anal.201174388438952802974 – reference: UpadhyayBBGhoshATreanţăSOptimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems on Hadamard manifoldsBull. Iran. Math. Soc.20234945460551410.1007/s41980-023-00791-7 – reference: HamdiAMishraSKMishraSKDecomposition methods based on augmented Lagrangians: a surveyTopics in Nonconvex Optimization2011New YorkSpringer175203 – reference: MishraSKUpadhyayBBPseudolinear Functions and Optimization2019LondonChapman and Hall/CRC – reference: Upadhyay, B.B., Ghosh, A., Treanţă, S.: Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds. Submitted in J. Glob. Optim. (2022) – reference: MishraSKSinghVLahaVMohapatraRNXuHWangSWuSYOn constraint qualifications for multiobjective optimization problems with vanishing constraintsOptimization Methods, Theory and Applications2015HeidelbergSpringer95135 – reference: BoumalNMishraBAbsilP-ASepulchreRManopt, a Matlab toolbox for optimization on manifoldsJ. Mach. Learn. Res.201415114551459 – reference: TreanSUpadhyayBBGhoshANonlaoponKOptimality conditions for multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifoldsMathematics2022103516 – reference: PennecXPennecXSommerSFletcherTManifold-valued image processing with SPD matricesRiemannian Geometric Statistics in Medical Image Analysis2020AmsterdamElsevier75134 – reference: BelkinMNiyogiPSemi-supervised learning on Riemannian manifoldsMach. Learn.2004561209239 – reference: MishraSKLagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programmingOptimization1996382931051410216 – reference: Ruiz-GarzónGOsuna-GómezRRufián-LizanaAHernández-JiménezBOptimality and duality on Riemannian manifoldsTaiwan J. Math.201822124512593859374 – reference: Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. Berkeley (1950) – reference: BaraniAOn pseudoconvex functions in Riemannian manifoldsJ. Finsler Geom. Appl.20212214224596892 – reference: FerreiraOPLouzeiroMSPrudenteLGradient method for optimization on Riemannian manifolds with lower bounded curvatureSIAM J. Optim.2019294251725414018420 – reference: UdrişteCConvex Functions and Optimization Methods on Riemannian Manifolds2013BerlinSpringer – reference: JouraniAConstraint qualifications and Lagrange multipliers in nondifferentiable programming problemsJ. Optim. Theory Appl.1994815335481281737 – reference: RapcsákTSmooth Nonlinear Optimization in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R} }^n$$\end{document}2013BerlinSpringer – reference: Fletcher, P.T., Moeller, J., Phillips, J.M., Venkatasubramanian, S.: Horoball hulls and extents in positive definite space. In: Algorithms and Data Structures, pp. 386–398 (2011) – reference: LedyaevYSZhuQJNonsmooth analysis on smooth manifoldsTrans. Am. Math. Soc.2007359368737322302512 – reference: UpadhyayBBTreanţăSMishraPOn Minty variational principle for nonsmooth multiobjective optimization problems on Hadamard manifoldsOptimization202210.1080/02331934.2022.2088369 – reference: UpadhyayBBGhoshAOn constraint qualifications for mathematical programming problems with vanishing constraints on Hadamard manifoldsJ. Optim. Theory Appl.2023465105810.1007/s10957-023-02207-2 – reference: TungLTTamDHOptimality conditions and duality for multiobjective semi-infinite programming on Hadamard manifoldsBull. Iran. Math. Soc.202248219122194487705 – reference: GrohsPHosseiniSϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-subgradient algorithms for locally Lipschitz functions on Riemannian manifoldsAdv. Comput. Math.20164223333603477792 – reference: MaedaTConstraint qualifications in multiobjective optimization problems: differentiable caseJ. Optim. Theory Appl.19948034835001265172 – reference: PredaVChiescuIOn constraint qualification in multiobjective optimization problems: semidifferentiable caseJ. Optim. Theory Appl.19991004174331673442 – reference: MishraSKMukherjeeRNGeneralized convex composite multiobjective nonsmooth programming and conditional proper efficiencyOptimization19953453661337615 – reference: MishraSKWangSYLaiKKOptimality and duality for multiple objective optimization under generalized type I univexityJ. Math. Anal. Appl.20053033153262113884 – reference: SteinOOn constraint qualifications in nonsmooth optimizationJ. Optim. Theory Appl.20041216476712084347 – reference: AbsilP-AMahonyRSepulchreROptimization Algorithms on Matrix Manifolds2008PrincetonPrinceton University Press – reference: ChryssochoosIVinterRBOptimal control problems on manifolds: a dynamic programming approachJ. Math. Anal. Appl.20032871181402010261 – reference: Papa QuirozEAQuispeEMOliveiraPRSteepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifoldsJ. Math. Anal. Appl.200934114674772394099 – reference: BergmannRHerzogRIntrinsic formulation of KKT conditions and constraint qualifications on smooth manifoldsSIAM J. Optim.2019294242324444014790 – reference: ChenS-IFangC-JVector variational inequality with pseudoconvexity on Hadamard manifoldsOptimization201665206720803564905 – reference: Papa QuirozEABaygorrea CusihuallpaNMaculanNInexact proximal point methods for multiobjective quasiconvex minimization on Hadamard manifoldsJ. Optim. Theory Appl.202018638798984142932 – reference: GolestaniMNobakhtianSNonsmooth multiobjective programming and constraint qualificationsOptimization20136267837953060962 – volume: 38 start-page: A567 year: 2016 ident: 2301_CR6 publication-title: SIAM J. Sci. Comput. doi: 10.1137/15M101988X – volume: 38 start-page: 255 year: 2004 ident: 2301_CR20 publication-title: RAIRO-Oper. Res. doi: 10.1051/ro:2004023 – start-page: 75 volume-title: Riemannian Geometric Statistics in Medical Image Analysis year: 2020 ident: 2301_CR46 doi: 10.1016/B978-0-12-814725-2.00010-8 – volume-title: Convex Analysis and Optimization in Hadamard Spaces year: 2014 ident: 2301_CR7 doi: 10.1515/9783110361629 – volume: 15 start-page: 1455 issue: 1 year: 2014 ident: 2301_CR11 publication-title: J. Mach. Learn. Res. – volume: 10 start-page: 3516 year: 2022 ident: 2301_CR51 publication-title: Mathematics doi: 10.3390/math10193516 – volume: 195 start-page: 596 issue: 2 year: 2022 ident: 2301_CR10 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-022-02107-x – volume: 48 start-page: 2191 year: 2022 ident: 2301_CR52 publication-title: Bull. Iran. Math. Soc. doi: 10.1007/s41980-021-00646-z – volume: 74 start-page: 3884 year: 2011 ident: 2301_CR26 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.02.023 – start-page: 175 volume-title: Topics in Nonconvex Optimization year: 2011 ident: 2301_CR25 doi: 10.1007/978-1-4419-9640-4_11 – volume: 62 start-page: 783 issue: 6 year: 2013 ident: 2301_CR22 publication-title: Optimization doi: 10.1080/02331934.2012.679939 – year: 2023 ident: 2301_CR54 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-023-02207-2 – volume: 16 start-page: 49 year: 2009 ident: 2301_CR44 publication-title: J. Convex Anal. – volume: 31 start-page: 781 issue: 3 year: 2017 ident: 2301_CR24 publication-title: Filomat doi: 10.2298/FIL1703781G – volume: 303 start-page: 315 year: 2005 ident: 2301_CR40 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.08.036 – year: 2023 ident: 2301_CR56 publication-title: Asia Pac. J. Oper. Res. doi: 10.1142/S0217595923500197 – volume: 77 start-page: 661 year: 2020 ident: 2301_CR16 publication-title: J. Glob. Optim. doi: 10.1007/s10898-020-00889-w – volume: 67 start-page: 154 year: 2007 ident: 2301_CR3 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2006.04.019 – volume: 56 start-page: 2037 issue: 4 year: 2022 ident: 2301_CR55 publication-title: RAIRO Oper. Res. doi: 10.1051/ro/2022098 – volume: 56 start-page: 209 issue: 1 year: 2004 ident: 2301_CR8 publication-title: Mach. Learn. doi: 10.1023/B:MACH.0000033120.25363.1e – volume: 29 start-page: 2423 issue: 4 year: 2019 ident: 2301_CR9 publication-title: SIAM J. Optim. doi: 10.1137/18M1181602 – volume-title: Optimization Algorithms on Matrix Manifolds year: 2008 ident: 2301_CR1 doi: 10.1515/9781400830244 – ident: 2301_CR29 doi: 10.1525/9780520411586-036 – volume: 106 start-page: 373 year: 2000 ident: 2301_CR31 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1004607615343 – volume: 100 start-page: 417 year: 1999 ident: 2301_CR41 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021794505701 – volume: 2014 start-page: Art. ID 524698, year: 2014 ident: 2301_CR13 publication-title: J. Appl. Math. – volume: 287 start-page: 118 year: 2003 ident: 2301_CR14 publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(03)00535-3 – volume: 181 start-page: 149 issue: 1 year: 2020 ident: 2301_CR35 publication-title: Math. Program. doi: 10.1007/s10107-019-01380-5 – volume: 18 start-page: 483 issue: 2 year: 2012 ident: 2301_CR45 publication-title: ESAIM Control Optim. Cal. Var. doi: 10.1051/cocv/2011102 – volume: 183 start-page: 85 year: 2019 ident: 2301_CR28 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-019-01539-2 – volume: 359 start-page: 3687 year: 2007 ident: 2301_CR30 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-07-04075-5 – ident: 2301_CR34 doi: 10.1137/1.9781611971255 – volume: 11 start-page: 1037 year: 2019 ident: 2301_CR49 publication-title: Symmetry doi: 10.3390/sym11081037 – volume-title: Smooth Nonlinear Optimization in $${\mathbb{R} }^n$$ year: 2013 ident: 2301_CR47 – start-page: 95 volume-title: Optimization Methods, Theory and Applications year: 2015 ident: 2301_CR38 doi: 10.1007/978-3-662-47044-2_6 – volume: 81 start-page: 533 year: 1994 ident: 2301_CR27 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02193099 – volume: 49 start-page: 45 year: 2023 ident: 2301_CR58 publication-title: Bull. Iran. Math. Soc. doi: 10.1007/s41980-023-00791-7 – volume: 38 start-page: 93 issue: 2 year: 1996 ident: 2301_CR36 publication-title: Optimization doi: 10.1080/02331939608844241 – volume-title: Convex Functions and Optimization Methods on Riemannian Manifolds year: 2013 ident: 2301_CR53 – volume: 10 start-page: 415 year: 2014 ident: 2301_CR60 publication-title: Pac. J. Optim. – volume: 42 start-page: 333 issue: 2 year: 2016 ident: 2301_CR23 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-015-9426-z – volume: 80 start-page: 483 issue: 3 year: 1994 ident: 2301_CR33 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02207776 – ident: 2301_CR57 doi: 10.1142/S0217595923500197 – volume: 29 start-page: 2517 issue: 4 year: 2019 ident: 2301_CR18 publication-title: SIAM J. Optim. doi: 10.1137/18M1180633 – volume: 53 start-page: 77 year: 2004 ident: 2301_CR15 publication-title: Optimization doi: 10.1080/02331930410001661505 – volume: 186 start-page: 879 issue: 3 year: 2020 ident: 2301_CR42 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-020-01725-7 – volume: 2 start-page: 14 issue: 2 year: 2021 ident: 2301_CR5 publication-title: J. Finsler Geom. Appl. – volume: 313 start-page: 587 year: 2006 ident: 2301_CR17 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.08.049 – volume: 341 start-page: 467 issue: 1 year: 2009 ident: 2301_CR43 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.10.010 – volume: 15 start-page: 26 year: 2013 ident: 2301_CR4 publication-title: Differ. Geom. Dyn. Syst. – volume: 7 start-page: 1291 issue: 3 year: 2021 ident: 2301_CR32 publication-title: Eur. J. Math. doi: 10.1007/s40879-021-00469-6 – volume: 17 start-page: 288 issue: 2 year: 2009 ident: 2301_CR21 publication-title: Top doi: 10.1007/s11750-008-0058-z – volume: 65 start-page: 2067 year: 2016 ident: 2301_CR12 publication-title: Optimization doi: 10.1080/02331934.2016.1235161 – volume: 22 start-page: 1245 year: 2018 ident: 2301_CR48 publication-title: Taiwan J. Math. doi: 10.11650/tjm/180501 – volume-title: Pseudolinear Functions and Optimization year: 2019 ident: 2301_CR39 – volume: 220 start-page: 304 year: 2005 ident: 2301_CR2 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2004.10.008 – volume: 34 start-page: 53 year: 1995 ident: 2301_CR37 publication-title: Optimization doi: 10.1080/02331939508844093 – year: 2022 ident: 2301_CR59 publication-title: Optimization doi: 10.1080/02331934.2022.2088369 – ident: 2301_CR19 doi: 10.1007/978-3-642-22300-6_33 – volume: 121 start-page: 647 year: 2004 ident: 2301_CR50 publication-title: J. Optim. Theory Appl. doi: 10.1023/B:JOTA.0000037607.48762.45
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Snippet	This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized...
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SubjectTerms	Applications of Mathematics Applied mathematics Banach spaces Calculus of Variations and Optimal Control; Optimization Constraints Convex analysis Engineering Euclidean space Geometry Manifolds Mathematical programming Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimality criteria Optimization Pareto optimum Qualifications Theory of Computation
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Title	Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds
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