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Steepest descent methods for multicriteria optimization

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  1. 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).
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Chen, Wang & Yang, Xinmin & Zhao, Yong, 2023. "Memory gradient method for multiobjective optimization," Applied Mathematics and Computation, Elsevier, vol. 443(C).
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. Zhe Chen, 2011. "Generalized viscosity approximation methods in multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 49(1), pages 179-192, May.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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).
  28. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  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. 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.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. 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.
  51. 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.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. Mounir El Maghri & Youssef Elboulqe, 2018. "Reduced Jacobian Method," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 917-943, December.
  64. 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.
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