On controlled Stampacchia-type vector variational inequalities

Cristina-Mihaela Cebuc; Savin Treanţă

doi:10.2478/candc-2024-0013

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On controlled Stampacchia-type vector variational inequalities

Control and Cybernetics

Volume 53 (2024): Issue 2 (June 2024)

By: Cristina-Mihaela Cebuc and Savin Treanţă

Open Access

|Feb 2025

Abstract

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.

References

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.
Search in Google Scholar Back to article
Ansari, Q. H. and Lee, G. M. (2010) Nonsmooth vector optimization problems and Minty vector variational inequalities. J. Optim. Theory Appl., 145, 1–16.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Crespi, G. P., Ginchev, I. and Rocca, M. (2008) Some remarks on the Minty vector variational principle. J. Math. Anal. Appl., 345, 165–175.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Hanson, M. A. (1964) Bounds for functionally convex optimal control problems. J. Math. Anal. Appl., 8, 84–89.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Jayswal, A. and Singh, S. (2017) Multiobjective variational problems and generalized vector variational-type inequalities. RAIRO Oper. Res., 51, 211–225.
Search in Google Scholar Back to article
Kim, M.H. (2004) Relations between vector continuous-time program and vector variational-type inequality. J. Appl. Math. Comput., 16, 279–287.
Search in Google Scholar Back to article
Lee, G.M. (2000) On Relations between Vector Variational Inequality and Vector Optimization Problem. Progress in Optim., 39, 167–179.
Search in Google Scholar Back to article
Miholca, M. (2014) On set-valued optimization problems and vector variational-like inequalities. Optim. Lett., 30, 101–108.
Search in Google Scholar Back to article
Oveisiha, M., and Zafarani, J. (2013) Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces. Optim. Lett., 7, 709–721.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Treanţă, S. and Guo, Y. (2023) The study of certain optimization problems via variational inequalities. Res. Math. Sci., 10, 7.
Search in Google Scholar Back to article
Treanţă, S., Antczak, T. and Saeed, T. (2023) Connections between non-linear optimization problems and associated variational inequalities. Mathematics, 11, 6, 1314.
Search in Google Scholar Back to article
Treanţă, S., and Saeed, T. (2023) On Weak Variational Control Inequalities via Interval Analysis. Mathematics, 11, 9, 2177.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Yu, S. J. and Yao, J. C. (1996) On vector variational inequalities. J. Optim. Theory Appl., 89, 749–769.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/candc-2024-0013 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 321 - 334

Published on: Feb 5, 2025

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

extremization problem,

preconvexity,

variational inequality,

(strictly) strong convexity,

control

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2025 Cristina-Mihaela Cebuc, Savin Treanţă, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 53 (2024): Issue 2 (June 2024)