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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 9
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Original Articles

Optimization of third-order discrete and differential inclusions described by polyhedral set-valued mappings

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Pages 1831-1844 | Received 25 May 2015, Accepted 15 Jul 2015, Published online: 11 Aug 2015

References

  • Mahmudov EN. Approximation and optimization of discrete and differential inclusions. Waltham (MA): Elsevier; 2011.
  • Aubin J-P, Frankowska H. Set-valued analysis. Boston (MA): Birkh\"{a}user; 1990.
  • Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
  • Ioffe AD, Tikhomirov VM. Theory of extremal problems. Moscow: Nauka; 1974. English trans., North-Holland, Amsterdam, 1978.
  • Kurzhanski AB, Veliov VM, editors. Set-valued analysis and differential inclusions. Boston, MA: Birkh\"{a}user; 1993.
  • Mahmudov EN. Optimization of discrete inclusions with distributed parameters. Optimization. 1990;21:197–207.
  • Mahmudov EN. Necessary and sufficient conditions for discrete and differential inclusions of elliptic type. J. Math. Anal. Appl. 2006;323:768–789.
  • Mahmudov EN. Sufficient conditions for optimality for differential inclusions of parabolic type and duality. J. Global Optim. 2008;41:31–42.
  • Mahmudov EN. On duality in problems of optimal control described by convex differential inclusions of Goursat-Darboux type. J. Math. Anal. Appl. 2005;307:628–640.
  • Mahmudov EN, Pshenichnyi BN. Necessary condition of extremum and evasion problem. Kiev: Institute Cybernetcis of Ukraine SSR; Preprint 1978; p. 3–22.
  • Mahmudov EN. The optimality principle for discrete and first order differential inclusions. J. Math. Anal. Appl. 2005;308:605–619.
  • Mordukhovich BS. Variational analysis and generalized differentiation, Vols. I and II. Berlin: Springer; 2006.
  • Rockafellar RT. Variational analysis and its applications. Set-Valued Anal. ( Preface to a special issue). 2002;12:1–4.
  • Affane D, Azzam-Laouir D. A control problem governed by a second-order differential inclusion. Appl. Anal. 2009;88:1677–1690.
  • Agarwal RP, O’Regan D. Viable solutions of differential inclusions on closed sets. Appl. Anal. 2004;83:1027–1036.
  • Auslender A, Mechler J. Second order viability problems for differential inclusions. J. Math. Anal. Appl. 1994;181:205–218.
  • Benchohra M, Ouahab A. Initial boundary value problems for second order impulsive functional differential inclusions. E. J. Qualitative Theory Diff. Equ. 2003;3:1–10.
  • Cernea A. On the existence of viable solutions for a class of second order differential inclusions. Discuss. Math. Differ. Incl. 2002;22:67–68.
  • Cubiotti P, Yao J-C. Two-point problem for vector differential inclusions with discontinuous right-hand side. Appl. Anal. 2014;93:1811–1823.
  • Haddad T, Yarou M. Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space. Electron. J. Differ. Equ. 2006;33:1–8.
  • Kuttler K. Evolution inclusions for time dependent families of subgradients. Appl. Anal. 2000;76:185–201.
  • Kyritsi S, Matzakos N, Papageorgiou NS. Periodic problems for strongly nonlinear second-order differential inclusions. J. Differ. Equ. 2002;183:279–302.
  • Ladas G, Lakshmikanthan V. Asymptotic equilibrium of ordinary differential systems. Appl. Anal. 2000;5:33–39.
  • Loewen PD, Rockafellar RT. Bolza problems with general time constraints. SIAM J. Control Optim. 1997;35:2050–2069.
  • Lupulescu V. A viability result for nonconvex second order differential inclusions. Electron. J. Differ. Equ. 2002;76:1–12.
  • Marco L, Murillo JA. Lyapunov functions for second-order differential inclusions: A viability approach. J. Math. Anal. Appl. 2001;262:339–354.
  • Pshenichnyi BN. Convex analysis and extremal problems. Moscow: Nauka; 1980.

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