A modified quasi-Newton method for uncertain multiobjective optimization problems under a finite uncertainty set

References

• Ansary, Md Abu Talhamainuddin, and Geetanjali Panda. 2015. “A Modified Quasi-Newton Method for Vector Optimization Problem.” Optimization 64 (11): 2289–2306. https://doi.org/10.1080/02331934.2014.947500.
   Web of Science ®Google Scholar
• Ansary, Md Abu Talhamainuddin, and Geetanjali Panda. 2019. “A Sequential Quadratically Constrained Quadratic Programming Technique for a Multi-Objective Optimization Problem.” Engineering Optimization 51 (1): 22–41. https://doi.org/10.1080/0305215X.2018.1437154.
   Web of Science ®Google Scholar
• Ansary, Md Abu Talhamainuddin, and Geetanjali Panda. 2021. “A Globally Convergent SQCQP Method for Multiobjective Optimization Problems.” SIAM Journal on Optimization 31 (1): 91–113. https://doi.org/10.1137/18M1182152.
   Web of Science ®Google Scholar
• Bazaraa, Mokhtar S., and Jamie J. Goode. 1982. “An Algorithm for Solving Linearly Constrained Minimax Problems.” European Journal of Operational Research 11 (2): 158–166. https://doi.org/10.1016/0377-2217(82)90110-2.
   Web of Science ®Google Scholar
• Ben-Tal, Aharon, Laurent El Ghaoui, and Arkadi Nemirovski. 2009. Robust Optimization. Princeton, NJ: Princeton University Press. https://books.google.co.uk/books/about/Robust_Optimization.html?id=DttjR7IpjUEC&redir_esc=y.
   Google Scholar
• Ben-Tal, Aharon, and Arkadi Nemirovski. 2008. “Selected Topics in Robust Convex Optimization.” Mathematical Programming 112:125–158. https://doi.org/10.1007/s10107-006-0092-2.
   Web of Science ®Google Scholar
• Dhara, Anulekha, and Joydeep Dutta. 2011. Optimality Conditions in Convex Optimization: A Finite-Dimensional View. Boca Raton, FL: CRC Press. https://doi.org/10.1201/b11156.
   Google Scholar
• Drummond, L. M. Graña, and Benar F. Svaiter. 2005. “A Steepest Descent Method for Vector Optimization.” Journal of Computational and Applied Mathematics 175 (2): 395–414. https://doi.org/10.1016/j.cam.2004.06.018.
   Web of Science ®Google Scholar
• Ehrgott, Matthias. 2005. Multicriteria Optimization. Berlin: Springer. https://doi.org/10.1007/3-540-27659-9.
   Google Scholar
• Ehrgott, Matthias, Jonas Ide, and Anita Schöbel. 2014. “Minmax Robustness for Multi-Objective Optimization Problems.” European Journal of Operational Research 239 (1): 17–31. https://doi.org/10.1016/j.ejor.2014.03.013.
   Web of Science ®Google Scholar
• Fishburn, Peter C. 1974. “Exceptional Paper–Lexicographic Orders, Utilities and Decision Rules: A Survey.” Management Science 20 (11): 1442–1471. https://doi.org/10.1287/mnsc.20.11.1442.
   Web of Science ®Google Scholar
• Fliege, J., L. M. Graña Drummond, and B. F. Svaiter. 2009. “Newton's Method for Multiobjective Optimization.” SIAM Journal on Optimization 20 (2): 602–626. https://doi.org/10.1137/08071692X.
   Web of Science ®Google Scholar
• Fliege, J., and B. Svaiter. 2000. “Steepest Descent Methods for Multicriteria Optimization.” Mathematical Methods of Operations Research 51 (3): 479–494. https://doi.org/10.1007/s001860000043.
   Web of Science ®Google Scholar
• Fliege, Jörg, and Ralf Werner. 2014. “Robust Multiobjective Optimization & Applications in Portfolio Optimization.” European Journal of Operational Research 234 (2): 422–433. https://doi.org/10.1016/j.ejor.2013.10.028.
   Web of Science ®Google Scholar
• Fukuda, Ellen H., and Luis Mauricio Graña Drummond. 2014. “A Survey on Multiobjective Descent Methods.” Pesquisa Operacional 34 (3): 585–620. https://doi.org/10.1590/0101-7438.2014.034.03.0585.
   Google Scholar
• Gass, Saul, and Thomas Saaty. 1955. “The Computational Algorithm for the Parametric Objective Function.” Naval Research Logistics Quarterly 2 (1-2): 39–45. https://doi.org/10.1002/nav.v2:1/2.
   Google Scholar
• Gebken, Bennet, and Sebastian Peitz. 2021. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications 188:696–723. https://doi.org/10.1007/s10957-020-01803-w.
   Web of Science ®Google Scholar
• Ghosh, Debdas, and Debjani Chakraborty. 2014. “A New Pareto Set Generating Method for Multi-Criteria Optimization Problems.” Operations Research Letters 42 (8): 514–521. https://doi.org/10.1016/j.orl.2014.08.011.
   Web of Science ®Google Scholar
• Göpfert, Alfred, and Reinhard Nehse. eds. 1990. Vektoroptimierung: Theorie, Verfahren und Anwendungen. Vol. 74 of Mathematisch-Naturwissenschaftliche Bibliothek. Leipzig, Germany: Teubner. https://puma.ub.uni-stuttgart.de/bibtex/2ba8e1c52f429ef4da38846abe5f0e909/roberta.toscano.
   Google Scholar
• Guo, Yating, Guoju Ye, Wei Liu, Dafang Zhao, and Savin Treanţă. 2023. “Solving Nonsmooth Interval Optimization Problems Based on Interval-Valued Symmetric Invexity.” Chaos, Solitons & Fractals174:113834. https://doi.org/10.1016/j.chaos.2023.113834.
   Web of Science ®Google Scholar
• Haimes, Yacov. 1971. “On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization.” IEEE Transactions on Systems, Man, and Cybernetics SMC-1 (3): 296–297. 10.1109/TSMC.1971.4308298.
   Google Scholar
• Kumar, S., M. A. T. Ansary, N. K. Mahato, D. Ghosh, and Y. Shehu. 2023. “Newton's Method for Uncertain Multiobjective Optimization Problems Under Finite Uncertainty Set.” Journal of Nonlinear and Variational Analysis 7 (5): 785–809. https://doi.org/10.23952/jnva.7.2023.5.08.
   Web of Science ®Google Scholar
• Kumar, S., N. K. Mahato, Md A. T. Ansary, and D. Ghosh. 2023. “A Quasi-Newton Method for Uncertain Multiobjective Optimization Problems via Robust Optimization Approach.” arXiv: 2310.07226.
   Google Scholar
• Kuroiwa, Daishi, and Gue Myung Lee. 2012. “On Robust Multiobjective Optimization.” Journal of Nonlinear and Convex Analysis 40 (2-3): 305–317. https://www.researchgate.net/publication/264994106_On_robust_multiobjective_optimization
   Google Scholar
• Lai, Kin Keung, Shashi Kant Mishra, and Bhagwat Ram. 2020. “On q-Quasi-Newton Method for Unconstrained Multiobjective Optimization Problems.” Mathematics 8 (4): 616. https://doi.org/10.3390/math8040616.
   Web of Science ®Google Scholar
• Lapucci, Matteo, and Pierluigi Mansueto. 2023. “A Limited Memory Quasi-Newton Approach for Multi-Objective Optimization.” Computational Optimization and Applications 85 (1): 33–73. https://doi.org/10.1007/s10589-023-00454-7.
   Web of Science ®Google Scholar
• Luc, Dinh The. 1989. Theory of Vector Optimization. Vol. 319 of the Book Series Lecture Notes in Economics and Mathematical Systems. Berlin: Springer. https://doi.org/10.1007/978-3-642-50280-4.
   Google Scholar
• Mahdavi-Amiri, N., and F. Salehi Sadaghiani. 2020. “A Superlinearly Convergent Nonmonotone Quasi-Newton Method for Unconstrained Multiobjective Optimization.” Optimization Methods and Software 35 (6): 1223–1247. https://doi.org/10.1080/10556788.2020.1737691.
   Web of Science ®Google Scholar
• Mäkelä, Marko M., Ville-Pekka Eronen, and Napsu Karmitsa. 2014. “On Nonsmooth Multiobjective Optimality Conditions with Generalized Convexities.” In Optimization in Science and Engineering: In Honor of the 60th Birthday of Panos M. Pardalos, 333–357. New York: Springer. https://doi.org/10.1007/978-1-4939-0808-0_17.
   Google Scholar
• Miettinen, Kaisa. 1998. Nonlinear Multiobjective Optimization. New York: Springer. https://doi.org/10.1007/978-1-4615-5563-6.
   Google Scholar
• Mishra, Shashi Kant, Giorgio Giorgi, and Shou-Yang Wang. 2004. “Duality in Vector Optimization in Banach Spaces with Generalized Convexity.” Journal of Global Optimization 29 (4): 415. https://doi.org/10.1023/B:JOGO.0000047911.03061.88.
   Web of Science ®Google Scholar
• Mishra, S. K., and R. N. Mukherjee. 1995. “Generalized Convex Composite Multi-Objective Nonsmooth Programming and Conditional Proper Efficiency.” Optimization 34 (1): 53–66. https://doi.org/10.1080/02331939508844093.
   Google Scholar
• Mishra, Shashi Kant, and Balendu Bhooshan Upadhyay. 2014. Pseudolinear Functions and Optimization. New York: Chapman & Hall/CRC. https://doi.org/10.1201/b17898.
   Google Scholar
• Mishra, Shashi K., Shouyang Wang, and Kin Keung Lai. 2007. V-Invex Functions and Vector Optimization. New York: Springer. https://doi.org/10.1007/978-0-387-75446-8.
   Google Scholar
• Mititelu, Ştefan, and Savin Treanţă. 2018. “Efficiency Conditions in Vector Control Problems Governed by Multiple Integrals.” Journal of Applied Mathematics and Computing 57 (1–2): 647–665. https://doi.org/10.1007/s12190-017-1126-z.
   Web of Science ®Google Scholar
• Morovati, Vahid, Hadi Basirzadeh, and Latif Pourkarimi. 2018. “Quasi-Newton Methods for Multiobjective Optimization Problems.” 4OR. A Quarterly Journal of Operations Research 16:261–294. https://doi.org/10.1007/s10288-017-0363-1.
   Google Scholar
• Nocedal, J., and S. T. Wright. 2006. Numerical Optimization. New York: Springer. https://books.google.co.uk/books/about/Numerical_Optimization.html?id=VbHYoSyelFcC&redir_esc=y.
   Google Scholar
• Povalej, Žiga. 2014. “Quasi-Newton Method for Multiobjective Optimization.” Journal of Computational and Applied Mathematics 255:765–777. https://doi.org/10.1016/j.cam.2013.06.045.
   Web of Science ®Google Scholar
• Qu, Shaojian, Mark Goh, and Felix T. S. Chan. 2011. “Quasi-Newton Methods for Solving Multiobjective Optimization.” Operations Research Letters 39 (5): 397–399. https://doi.org/10.1016/j.orl.2011.07.008.
   Web of Science ®Google Scholar
• Qu, Shaojian, Chen Liu, Mark Goh, Yijun Li, and Ying Ji. 2014. “Nonsmooth Multiobjective Programming with Quasi-Newton Methods.” European Journal of Operational Research 235 (3): 503–510. https://doi.org/10.1016/j.ejor.2014.01.022.
   Web of Science ®Google Scholar
• Saeed, Tareq, and Savin Treanţă. 2023. “On Sufficiency Conditions for Some Robust Variational Control Problems.” Axioms 12 (7): 705. https://doi.org/10.3390/axioms12070705.
   Web of Science ®Google Scholar
• Singh, Yadvendra, S. K. Mishra, and K. K. Lai. 2017. “Optimality and Duality for Nonsmooth Semi-Infinite Multiobjective Programming with Support Functions.” Yugoslav Journal of Operations Research 27 (2): 205–218. https://doi.org/10.2298/YJOR170121010S.
   Google Scholar
• Soyster, Allen L. 1973. “Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming.” Operations Research 21 (5): 1154–1157. https://doi.org/10.1287/opre.21.5.1154.
   Web of Science ®Google Scholar
• Treanţă, Savin. 2021. “Efficiency in Uncertain Variational Control Problems.” Neural Computing and Applications 33 (11): 5719–5732. https://doi.org/10.1007/s00521-020-05353-0.
   Web of Science ®Google Scholar