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Steepest descent methods for multicriteria optimization

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  1. Gonçalves, M.L.N. & Lima, F.S. & Prudente, L.F., 2022. "A study of Liu-Storey conjugate gradient methods for vector optimization," Applied Mathematics and Computation, Elsevier, vol. 425(C).
  2. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
  3. M. L. N. Gonçalves & F. S. Lima & L. F. Prudente, 2022. "Globally convergent Newton-type methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 83(2), pages 403-434, November.
  4. Rocha, Rogério Azevedo & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros & Souza, Michael, 2016. "Logarithmic quasi-distance proximal point scalarization method for multi-objective programming," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 856-867.
  5. Y. Bello-Cruz & J. G. Melo & L. F. Prudente & R. V. G. Serra, 2025. "A proximal gradient method with an explicit line search for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 92(2), pages 437-469, November.
  6. Orizon P. Ferreira & Mauricio S. Louzeiro & Leandro F. Prudente, 2020. "Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 507-533, February.
  7. J. Y. Bello Cruz & G. Bouza Allende, 2014. "A Steepest Descent-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 371-391, August.
  8. Stefan Banholzer & Giulia Fabrini & Lars Grüne & Stefan Volkwein, 2020. "Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
  9. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
  10. Kazemi, Abolghasem & Moreno, Jovita & Iribarren, Diego, 2023. "Economic optimization and comparative environmental assessment of natural gas combined cycle power plants with CO2 capture," Energy, Elsevier, vol. 277(C).
  11. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Proximal gradient methods for multiobjective optimization and their applications," Computational Optimization and Applications, Springer, vol. 72(2), pages 339-361, March.
  12. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2023. "An accelerated proximal gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 86(2), pages 421-455, November.
  13. Li, Xiang & Sun, Jian-Qiao, 2019. "Intersection multi-objective optimization on signal setting and lane assignment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1233-1246.
  14. Matteo Lapucci & Pierluigi Mansueto, 2023. "A limited memory Quasi-Newton approach for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 85(1), pages 33-73, May.
  15. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
  16. G. Bento & J. Cruz Neto & G. López & Antoine Soubeyran & J. Souza, 2018. "The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem," Post-Print hal-01985333, HAL.
  17. Zhou Wei & Qing Hai He, 2014. "Nonsmooth Steepest Descent Method by Proximal Subdifferentials in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 465-477, May.
  18. L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.
  19. Mercier, Quentin & Poirion, Fabrice & Désidéri, Jean-Antoine, 2018. "A stochastic multiple gradient descent algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 808-817.
  20. S. Liu & L. N. Vicente, 2024. "The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning," Annals of Operations Research, Springer, vol. 339(3), pages 1119-1148, August.
  21. G. Cocchi & M. Lapucci, 2020. "An augmented Lagrangian algorithm for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 29-56, September.
  22. G. C. Bento & J. X. Cruz Neto & P. S. M. Santos, 2013. "An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 108-124, October.
  23. G. Cocchi & G. Liuzzi & S. Lucidi & M. Sciandrone, 2020. "On the convergence of steepest descent methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 1-27, September.
  24. Jamilu Yahaya & Poom Kumam & Mahmoud Muhammad Yahaya, 2025. "A New Hybrid Conjugate Gradient Method Based on a Convex Combination for Multiobjective Optimization," SN Operations Research Forum, Springer, vol. 6(2), pages 1-26, June.
  25. Jiang, Yuanchun & Liu, Yezheng & Shang, Jennifer & Yildirim, Pinar & Zhang, Qingfu, 2018. "Optimizing online recurring promotions for dual-channel retailers: Segmented markets with multiple objectives," European Journal of Operational Research, Elsevier, vol. 267(2), pages 612-627.
  26. G. Cocchi & G. Liuzzi & A. Papini & M. Sciandrone, 2018. "An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints," Computational Optimization and Applications, Springer, vol. 69(2), pages 267-296, March.
  27. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
  28. Miglierina Enrico & Molho Elena & Recchioni Maria Cristina, 2006. "Box-constrained vector optimization: a steepest descent method without “a priori” scalarization," Economics and Quantitative Methods qf0603, Department of Economics, University of Insubria.
  29. Shahabeddin Najafi & Masoud Hajarian, 2023. "Multiobjective Conjugate Gradient Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1229-1248, June.
  30. P. B. Assunção & O. P. Ferreira & L. F. Prudente, 2021. "Conditional gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 78(3), pages 741-768, April.
  31. Zhe Chen, 2011. "Generalized viscosity approximation methods in multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 49(1), pages 179-192, May.
  32. Ellen H. Fukuda & L. M. Graña Drummond & Fernanda M. P. Raupp, 2016. "An external penalty-type method for multicriteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 493-513, July.
  33. Liu, Kaiping & Chen, Jiawei, 2026. "A projected PRP conjugate gradient method for constrained multiobjective optimization with application to friction stir welding," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 244(C), pages 70-89.
  34. Oliver Schütze & Víctor Adrián Sosa Hernández & Heike Trautmann & Günter Rudolph, 2016. "The hypervolume based directed search method for multi-objective optimization problems," Journal of Heuristics, Springer, vol. 22(3), pages 273-300, June.
  35. Kanako Mita & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Nonmonotone line searches for unconstrained multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 63-90, September.
  36. Balendu Bhooshan Upadhyay & Rupesh Krishna Pandey & Subham Poddar & Shengda Zeng, 2026. "Fletcher-reeves-type conjugate direction algorithm for interval-valued multiobjective optimization problems," Annals of Operations Research, Springer, vol. 359(3), pages 2389-2429, April.
  37. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
  38. Zhihao Li & Qingtao Wu & Moli Zhang & Lin Wang & Youming Ge & Guoyong Wang, 2025. "Stochastic Zeroth-Order Multi-Gradient Algorithm for Multi-Objective Optimization," Mathematics, MDPI, vol. 13(4), pages 1-31, February.
  39. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.
  40. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
  41. Andrea Cristofari & Marianna Santis & Stefano Lucidi, 2024. "On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 126-145, October.
  42. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
  43. Vieira, D.A.G. & Lisboa, A.C., 2019. "A cutting-plane method to nonsmooth multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 822-829.
  44. Alfredo N. Iusem & Jefferson G. Melo & Ray G. Serra, 2021. "A Strongly Convergent Proximal Point Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 183-200, July.
  45. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
  46. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
  47. Konstantin Sonntag & Bennet Gebken & Georg Müller & Sebastian Peitz & Stefan Volkwein, 2024. "A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 455-487, October.
  48. Chen, Wang & Yang, Xinmin & Zhao, Yong, 2023. "Memory gradient method for multiobjective optimization," Applied Mathematics and Computation, Elsevier, vol. 443(C).
  49. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
  50. Miglierina Enrico, 2003. "Stability of critical points for vector valued functions and Pareto efficiency," Economics and Quantitative Methods qf0301, Department of Economics, University of Insubria.
  51. M. L. N. Gonçalves & L. F. Prudente, 2020. "On the extension of the Hager–Zhang conjugate gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 889-916, July.
  52. Ceng, Lu-Chuan & Yao, Jen-Chih, 2007. "Approximate proximal methods in vector optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 1-19, November.
  53. Qingjie Hu & Ruyun Li & Yanyan Zhang & Zhibin Zhu, 2024. "On the Extension of Dai-Liao Conjugate Gradient Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 810-843, October.
  54. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
  55. Qing-Rui He & Sheng-Jie Li & Bo-Ya Zhang & Chun-Rong Chen, 2024. "A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 805-842, December.
  56. Mehri Rashidi & Majid Soleimani-damaneh, 2024. "MultiSQP-GS: a sequential quadratic programming algorithm via gradient sampling for nonsmooth constrained multiobjective optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 729-767, December.
  57. Chin-Hsiang Cheng & Yu-Ting Lin, 2020. "Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm," Energies, MDPI, vol. 13(19), pages 1-18, October.
  58. Chin-Hsiang Cheng & Yu-Ting Lin, 2022. "Computational Optimization of Free-Piston Stirling Engine by Variable-Step Simplified Conjugate Gradient Method with Compatible Strategies," Energies, MDPI, vol. 15(10), pages 1-16, May.
  59. G. C. Bento & J. X. Cruz Neto, 2013. "A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 125-137, October.
  60. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
  61. Brian Dandurand & Margaret M. Wiecek, 2016. "Quadratic scalarization for decomposed multiobjective optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1071-1096, October.
  62. Ana Luísa Custódio & Youssef Diouane & Rohollah Garmanjani & Elisa Riccietti, 2021. "Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 73-93, January.
  63. Mustapha El Moudden & Abdelkrim El Mouatasim, 2021. "Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 220-242, January.
  64. Mounir El Maghri & Youssef Elboulqe, 2018. "Reduced Jacobian Method," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 917-943, December.
  65. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.
  66. Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
  67. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
  68. X. M. Wang & J. H. Wang & C. Li, 2023. "Convergence of Inexact Steepest Descent Algorithm for Multiobjective Optimizations on Riemannian Manifolds Without Curvature Constraints," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 187-214, July.
  69. Mustapha El Moudden & Ahmed El Ghali, 2018. "A new reduced gradient method for solving linearly constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 719-741, December.
  70. Bento, G.C. & Cruz Neto, J.X. & Oliveira, P.R. & Soubeyran, A., 2014. "The self regulation problem as an inexact steepest descent method for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 235(3), pages 494-502.
  71. Qingjie Hu & Yanyan Zhang & Ruyun Li & Wanyou Cheng, 2026. "A Diagonal Quasi-Newton Method with Modified BFGS Update for Nonconvex Multiobjective Optimization," Journal of Global Optimization, Springer, vol. 94(1), pages 203-233, January.
  72. Suyun Liu & Luis Nunes Vicente, 2022. "Accuracy and fairness trade-offs in machine learning: a stochastic multi-objective approach," Computational Management Science, Springer, vol. 19(3), pages 513-537, July.
  73. Rogério A. Rocha & Paulo R. Oliveira & Ronaldo M. Gregório & Michael Souza, 2016. "A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 964-979, December.
  74. L. F. Prudente & D. R. Souza, 2022. "A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1107-1140, September.
  75. Qing-Rui He & Sheng-Jie Li & Ming-Hua Li & Chun-Rong Chen, 2026. "A nonlinear conjugate gradient algorithm for multiobjective optimization: multiple hybrid search direction and global rates," Computational Optimization and Applications, Springer, vol. 93(3), pages 1021-1067, April.
  76. Yong Zhao & Wang Chen & Xinmin Yang, 2024. "Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 215-241, January.
  77. G. A. Carrizo & N. S. Fazzio & M. D. Sánchez & M. L. Schuverdt, 2024. "Scaled-PAKKT sequential optimality condition for multiobjective problems and its application to an Augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 89(3), pages 769-803, December.
  78. Xiaopeng Zhao & Debdas Ghosh & Xiaolong Qin & Christiane Tammer & Jen-Chih Yao, 2025. "On the convergence analysis of a proximal gradient method for multiobjective optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 102-132, April.
  79. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.
  80. Chen, Jian & Tang, Liping & Yang, Xinmin, 2023. "A Barzilai-Borwein descent method for multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 196-209.
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