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On generalized KT-pseudoinvex control problems involving multiple integral functionals. (English) Zbl 1402.49020

Summary: In this paper, we introduce (strongly) \(b\)-KT-pseudoinvex multidimensional control problems. In this regard, we consider an extended condition of invexity and we prove that (strongly) \(b\)-KT-pseudoinvex multidimensional control problems are described such that all Kuhn-Tucker points are optimal solutions. As well, in order to illustrate our main characterization result and its effectiveness, we propose an application.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
46T20 Continuous and differentiable maps in nonlinear functional analysis
58J32 Boundary value problems on manifolds
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[1] V. M. Alekseev, M. V. Tikhomirov, S. V. Fomin, Commande Optimale, Mir, Moscow, 1982.; V. M. Alekseev, M. V. Tikhomirov, S. V. Fomin, Commande Optimale, Mir, Moscow, 1982.
[2] Antczak, T.; Arana-Jiménez, M., Sufficient optimality criteria and duality for multiobjective variational control problems with b-(p,r)-invex functions, Opusc. Math., 34, 4, 665-682, (2014) · Zbl 1330.65095
[3] Antczak, T.; Pitea, A., Parametric approach to multitime multiobjective fractional variational problems under (f, ρ)-convexity, Optim. Control Appl. Meth., 37, 5, 831-847, (2016) · Zbl 1348.90560
[4] Arana-Jiménez, M.; Osuna-Gómez, R.; Rufián-Lizana, A.; Ruiz-Garzón, G., KT-invex control problem, Appl. Math. Comput., 197, 2, 489-496, (2008) · Zbl 1152.49018
[5] Bhatia, D.; Kumar, P., Multiobjective control problem with generalized invexity, J. Math. Anal. Appl., 189, 3, 676-692, (1995) · Zbl 0831.90100
[6] Chandra, S.; Craven, B. D.; Husain, I., A class of nondifferentiable control problems, J. Optim. Theory Appl., 56, 2, 227-243, (1988) · Zbl 0621.49010
[7] Hanson, M. A., On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 80, 2, 545-550, (1981) · Zbl 0463.90080
[8] Jayswal, A.; Singh, S.; Kurdi, A., Multitime multiobjective variational problems and vector variational-like inequalities, Eur. J. Oper. Res., 254, 3, 739-745, (2016) · Zbl 1346.49012
[9] Martin, D. H., The essence of invexity, J. Optim. Theory Appl., 47, 1, 65-76, (1985) · Zbl 0552.90077
[10] Mititelu, Şt.; Treanţă, S., Efficiency conditions in vector control problems governed by multiple integrals, J. Appl. Math. Comput., 57, 1-2, 647-665, (2018) · Zbl 1391.49043
[11] Mond, B.; Hanson, M. A., Duality for control problems, SIAM J. Control, 6, 1, 114-120, (1968) · Zbl 0164.10707
[12] Mond, B.; Smart, I., Duality and sufficiency in control problems with invexity, J. Math. Anal. Appl., 136, 1, 325-333, (1988) · Zbl 0667.49001
[13] Nahak, C.; Nanda, S., Duality for variational problems with pseudo-invexity, Optimization, 34, 4, 365-371, (1995) · Zbl 0855.90121
[14] de Oliveira, V. A.; Silva, G. N.; Rojas-Medar, M. A., KT-invexity in optimal control problems, Nonlin. Anal. Theory Methods Appl., 71, 10, 4790-4797, (2009) · Zbl 1169.49017
[15] Preda, V., On duality and sufficiency in control problems with general invexity, Bull. Math. Soc. Sci. Math Roum., 35, 83, 271-280, (1991) · Zbl 0828.49021
[16] Treanţă, S., Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE, Comput. Math. Appl., 75, 2, 547-560, (2018) · Zbl 1408.37111
[17] Treanţă, S.; Arana-Jiménez, M., KT-pseudoinvex multidimensional control problem, Optim. Control Appl. Meth., 1-10, (2018) · Zbl 1398.93050
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