Details

Title

Efficiency in vector ratio variational control problems involving geodesic quasiinvex multiple integral functionals

Journal title

Archives of Control Sciences

Yearbook

2021

Volume

vol. 31

Issue

No 3

Authors

Affiliation

Treanţă, Savin : University “Politehnica”of Bucharest, Faculty of Applied Sciences, Department of Applied Mathematics, 313 Splaiul Independentei, 060042 – Bucharest, Romania ; Mititelu, Ştefan : Technical University of Civil Engineering, Department of Mathematics and Informatics, 124 Lacul Tei, 020396 – Bucharest, Romania

Keywords

multiobjective fractional control problem ; geodesic efficient solution ; (p; b)-geodesic quasiinvexity

Divisions of PAS

Nauki Techniczne

Coverage

687-706

Publisher

Committee of Automatic Control and Robotics PAS

Bibliography

[1] R.P. Agarwal, I. Ahmad, A. Iqbal, and S. Ali: Generalized invex sets and preinvex functions on Riemannian manifolds, Taiwanese J. Math., 16(5), (2012), 1719–1732, DOI: 10.11650/twjm/1500406792.
[2] T. Antczak: G-pre-invex functions in mathematical programming, J. Comput. Appl. Math., 217(1), (2008), 212–226, DOI: 10.1016/j.cam.2007.06.026.
[3] M. Arana-Jimenez, B. Hernandez-Jimenez, G. Ruiz-Garzon, and A. Rufian-Lizana: FJ-invex control problem, Appl. Math. Lett., 22(12), (2009), 1887–1891, DOI: 10.1016/j.aml.2009.07.016.
[4] A. Barani and M.R. Pouryayevali: Invex sets and preinvex functions on Riemannian manifolds, J. Math. Anal. Appl., 328(2), (2007), 767–779, DOI: 10.1016/j.jmaa.2006.05.081.
[5] M.A. Hanson: On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(2), (1981), 545–550, DOI: 10.1016/0022-247X(81)90123-2.
[6] R. Jagannathan: Duality for nonlinear fractional programs, Z. Oper. Res., 17(1-3), (1973), DOI: 10.1007/BF01951364.
[7] V. Jeyakumar: Strong and weak invexity in mathematical programming, Research report (University of Melbourne, Department of Mathematics), 1984, no. 29.
[8] D.H. Martin: The essence of invexity, J. Optim. Theory Appl., 47(1), (1985), 65–76, DOI: 10.1007/BF00941316.
[9] St. Mititelu: Optimality and duality for invex multi-time control problems with mixed constraints, J. Adv. Math. Stud., 2(1), (2009), 25–34.
[10] St. Mititelu, M.Constantinescu, and C. Udriste: Efficiency for multitime variational problems with geodesic quasiinvex functionals on Riemannian manifolds, BSG Proceedings 22. The Intern. Conf. “Differential Geometry – Dynamical Systems”, September 1-4, 2014, Mangalia-Romania, pp. 38–50. Balkan Society of Geometers, Geometry Balkan Press 2015.
[11] St. Mititelu and S. Treanta: Efficiency conditions in vector control problems governed by multiple integrals, J. Appl. Math. Comput., 57(1-2), (2018), 647–665, DOI: 10.1007/s12190-017-1126-z.
[12] M.A. Noor and K.I. Noor: Some characterizations of strongly preinvex functions, J. Math. Anal. Appl., 316(2), (2006), 697–706, DOI: 10.1016/ j.jmaa.2005.05.014.
[13] V.A. de Oliveira and G.N. Silva: On sufficient optimality conditions for multiobjective control problems, J. Global Optim., 64(4), (2016), 721–744, DOI: 10.1007/s10898-015-0351-y.
[14] R. Pini: Convexity along curves and indunvexity, Optimization, 29(4), (1994), 301–309, DOI: 10.1080/02331939408843959.
[15] T. Rapcsak: Smooth Nonlinear Optimization in Rn, Nonconvex Optimization and Its Applications, Kluwer Academic, 1997.
[16] W. Tang and X. Yang: The sufficiency and necessity conditions of strongly preinvex functions, OR Transactions, 10, 3, (2006), 50–58. [17] S. Treanta: PDEs of Hamilton-Pfaff type via multi-time optimization problems, U.P.B. Sci. Bull., Series A: Appl. Math. Phys., 76(1), (2014), 163–168.
[18] S. Treanta: Optimal control problems on higher order jet bundles. The Intern. Conf. “Differential Geometry – Dynamical Systems”, October 10- 13, 2013, Bucharest-Romania, pp. 181–192. Balkan Society of Geometers, Geometry Balkan Press 2014.
[19] S. Treanta: Multiobjective fractional variational problem on higherorder jet bundles, Commun. Math. Stat., 4(3), (2016), 323–340, DOI: 10.1007/s40304-016-0087-0.
[20] S. Treanta: Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE, Comput. Math. Appl., 75(2), (2018), 547–560, DOI: 10.1016/j.camwa.2017.09.033.
[21] S. Treanta and M. Arana-Jimenez: KT-pseudoinvex multidimensional control problem, Optim. Control Appl. Meth., 39(4), (2018), 1291–1300, DOI: 10.1002/oca.2410.
[22] S. Treanta and M. Arana-Jimenez: On generalized KT-pseudoinvex control problems involving multiple integral functionals, Eur. J. Control, 43, (2018), 39–45, DOI: 10.1016/j.ejcon.2018.05.004.
[23] S. Treanta: Efficiency in generalized V-KT-pseudoinvex control problems, Int. J. Control, 93(3), (2020), 611–618, DOI: 10.1080/00207179.2018.1483082.
[24] C. Udriste: Convex Functions and Optimization Methods on Riemannian Manifolds, Mathematics and Its Applications, KluwerAcademic, 297, 1994.
[25] T. Weir and B. Mond: Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 136(1), (1988), 29–38, DOI: 10.1016/0022-247X(88)90113-8.

Date

2021.09.27

Type

Article

Identifier

DOI: 10.24425/acs.2021.138697
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