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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 17
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Research Article

On a class of controlled differential variational inequalities

Pages 6191-6211 | Received 04 Aug 2020, Accepted 24 Nov 2020, Published online: 26 Apr 2021

References

  • Jagannathan R. Duality for nonlinear fractional programming. Z Oper Res. 1973;17:1–3.
  • Hanson MA. On sufficiency of Kuhn–Tucker conditions. J Math Anal Appl. 1981;80:545–550.
  • Martin DH. The essence of invexity. J Optim Theory Appl. 1985;47:65–76.
  • Mititelu Şt., Treană S. Efficiency conditions in vector control problems governed by multiple integrals. J Appl Math Comput. 2018;57:647–665.
  • Treană S, Arana-Jiménez M. On generalized KT-pseudoinvex control problems involving multiple integral functionals. Eur J Control. 2018;43:39–45.
  • Burke JV, Ferris MC. Weak sharp minima in mathematical programming. SIAM J Control Optim. 1993;31:1340–1359.
  • Marcotte P, Zhu D. Weak sharp solutions of variational inequalities. SIAM J Optim. 1998;9:179–189.
  • Patriksson M. A unified framework of descent algorithms for nonlinear programs and variational inequalities [PhD. Thesis]. Department of Mathematics, Linköping Institute of Technology, 1993.
  • Chen GY, Goh CJ, Yang XQ. On gap functions for vector variational inequalities. In: Giannessi F, editor. Vector variational inequality and vector equilibria. Mathematical Theories. Boston: Kluwer Academic Publishers; 2000. p. 55–72.
  • Wu Z, Wu SY. Weak sharp solutions of variational inequalities in Hilbert spaces. SIAM J Optim. 2004;14:1011–1027.
  • Hu YH, Song W. Weak sharp solutions for variational inequalities in Banach spaces. J Math Anal Appl. 2011;374:118–132.
  • Polyak BT. Introduction to optimization. Optimization Software, Publications Division, New York, 1987.
  • Oveisiha M, Zafarani J. Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces. Optim Lett. 2013;7:709–721.
  • Alshahrani M, Al-Homidan S, Ansari QH. Minimum and maximum principle sufficiency properties for nonsmooth variational inequalities. Optim Lett. 2016;10:805–819.
  • Liu Y, Wu Z. Characterization of weakly sharp solutions of a variational inequality by its primal gap function. Optim Lett. 2016;10:563–576.
  • Zhu SK. Weak sharp efficiency in multiobjective optimization. Optim Lett. 2016;10:1287–1301.
  • Kulkarni AA, Shanbhag UV. On the variational equilibrium as a refinement of the generalized Nash equilibrium. Automatica. 2012;48:45–55.
  • Villanueva ME, Quirynen R, Diehl M, et al. Robust MPC via min-max differential inequalities. Automatica. 2017;77:311–321.
  • Agrachev AA, Sachkov YL. Control theory from the geometric viewpoint. Springer-Verlag Berlin Heidelberg: Springer Science & Business Media; 2004.
  • Liberzon D. Calculus of variations and optimal control theory: A concise introduction. Princeton University Press; 2012.
  • Clarke FH. Functional analysis, calculus of variations and optimal control. London: Springer; 2013. (Graduate Texts in Mathematics, Vol. 264).
  • Treană S. PDEs of Hamilton–Pfaff type via multi-time optimization problems. UPB Sci Bull Ser A. 2014;76:163–168.
  • Treană S. Multiobjective fractional variational problem on higher-order jet bundles. Commun Math Stat. 2016;4:323–340.
  • Treană S. Higher-order Hamilton dynamics and Hamilton–Jacobi divergence PDE. Comput Math Appl. 2018;75:547–560.
  • Treană S. Constrained variational problems governed by second-order Lagrangians. Appl Anal. 2020;99:1467–1484.
  • Treană S. On controlled variational inequalities involving convex functionals. In Le Thi H, Le H, Pham Dinh T, editors, Optimization of complex systems: theory, models, algorithms and applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol. 991, Cham: Springer; 2020. p. 164–174.
  • Treană S. PDE-constrained vector variational problems governed by curvilinear integral functionals. Appl Anal Optim. 2019;3:83–101.
  • Treană S. Variational analysis with applications in optimisation and control. Newcastle upon Tyne, United Kingdom: Cambridge Scholars Publishing; 2019. ISBN: 978-1-5275-3728-6.
  • Treană S. On a modified optimal control problem with first-order PDE constraints and the associated saddle-point optimality criterion. Eur J Control. 2020;51:1–9.
  • Hiriart-Urruty J-B, Lemaréchal C. Fundamentals of convex analysis. Berlin: Springer; 2001.
  • Ferris MC, Mangasarian OL. Minimum principle sufficiency. Math Program. 1992;57:1–14.
  • Mangasarian OL, Meyer RR. Nonlinear perturbation of linear programs. SIAM J Control Optim. 1979;17:745–752.

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