On controlled Stampacchia-type vector variational inequalities

• Autorzy: Cebuc Cristina-Mihaela , Treanţă Savin

Identyfikatory

DOI

10.2478/candc-2024-0013

• Języki publikacji: EN

Abstrakty

EN

This paper establishes connections between new classes of generalized Stampacchia (weak) vector variational control inequalities and the corresponding multiple-objective extremization problems. In this regard, we introduce the concepts of (strictly) strong convexity and preconvexity, associated with controlled multiple integral type functionals, and a mean value type theorem.

Słowa kluczowe

EN

extremization problem; preconvexity; variational inequality; strong convexity; control

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2024
• Tom: Vol. 53, No. 2
• Strony: 321--334
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Cebuc Cristina-Mihaela

• Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

autor

Treanţă Savin

• Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
• Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
• Fundamental Sciences Applied in Engineering - Research Center (SFAI), National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

Bibliografia

• Al-Homidan, S. and Ansari, Q. H. (2010) Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems. J. Optim. Theory Appl., 144, 1–11.
• Ansari, Q. H. and Lee, G. M. (2010) Nonsmooth vector optimization problems and Minty vector variational inequalities. J. Optim. Theory Appl., 145, 1–16.
• Arana-Jiménez, M., Ruiz-Garzón, G., Rufián-Lizana, A. and Gómez, R. O. (2010) A necessary and sufficient condition for duality in multiobjective variational problems. Eur. J. Oper. Res., 201, 672–681.
• Crespi, G. P., Ginchev, I. and Rocca, M. (2004) Variational inequalities in vector optimization. In: F. Giannessi, A. Maugeri, eds., Variational Analysis and Applications. Kluwer Academic, Dordrecht, 79.
• Crespi, G. P., Ginchev, I. and Rocca, M. (2008) Some remarks on the Minty vector variational principle. J. Math. Anal. Appl., 345, 165–175.
• Giannessi, F. (1980) Theorems of alternative, quadratic programs and complementarity problems. In: R.W. Cottle, F. Giannessi, and J. L. Lions, eds., Variational Inequalities and Complementarity Problems, 42, 331–365, John Wiley and Sons, Chichester.
• Giannessi, F. (1998) On Minty variational principle. In: F. Gianessi et al., eds, New Trends in Math. Programming. Appl. Opt., APOP 13, 93–99. Kluwer Academic Publishers.
• Hanson, M. A. (1964) Bounds for functionally convex optimal control problems. J. Math. Anal. Appl., 8, 84–89.
• Jayswal, A., Singh, S. and Kurdi, A. (2016) Multitime multiobjective variational problems and vector variational-like inequalities. Eur. J. Oper. Res., 254(3), 739–745.
• Jayswal, A. and Singh, S. (2017) Multiobjective variational problems and generalized vector variational-type inequalities. RAIRO Oper. Res., 51, 211–225.
• Kim, M.H. (2004) Relations between vector continuous-time program and vector variational-type inequality. J. Appl. Math. Comput., 16, 279–287.
• Lee, G.M. (2000) On Relations between Vector Variational Inequality and Vector Optimization Problem. Progress in Optim., 39, 167–179.
• Miholca, M. (2014) On set-valued optimization problems and vector variational-like inequalities. Optim. Lett., 30, 101–108.
• Oveisiha, M., and Zafarani, J. (2013) GeneralizedMinty vector variational-like inequalities and vector optimization problems in Asplund spaces. Optim. Lett., 7, 709–721.
• Ruiz-Garzón, G., Santos, L. B., Rufián-Lizana, A. and Arana-Jiménez, M. (2010) Some relations between Minty variational-like inequality problems and vectorial optimization problems in Banach spaces. Comput. Math. Appl., 60, 2679–2688.
• Santos, L. B., Rojas-Medar, M. A. and Rufián-Lizana, A. (2006) Some relations between variational-like inequalities and efficient solutions of certain nonsmooth optimization problems. Int. J. Math. Math. Sci., 2006, 16.
• Treanţă, S. and Guo, Y. (2023) The study of certain optimization problems via variational inequalities. Res. Math. Sci., 10, 7.
• Treanţă, S., Antczak, T. and Saeed, T. (2023) Connections between non-linear optimization problems and associated variational inequalities. Mathematics, 11, 6, 1314.
• Treanţă, S., and Saeed, T. (2023) On Weak Variational Control Inequalities via Interval Analysis. Mathematics, 11, 9, 2177.
• Yang, X. M., Yang, X. Q. and Teo, K. L. (2004) Some Remarks on the Minty Vector Variational Inequality. J. Optim. Theory Appl., 121, 193–201.
• Yu, S. J. and Yao, J. C. (1996) On vector variational inequalities. J. Optim. Theory Appl., 89, 749–769.
• Yu, G. and Lu, Y. (2011) Multi-objective Optimization Problems and Vector Variational-like Inequalities Involving Semi-strong E-convexity. Fourth International Joint Conference on Computational Sciences and Optimization, Kunming and Lijiang City, 476–479. IEEE Computer Society.