Abstract
Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011)), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chinchuluun A., Pardalos P.M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154(1), 29–50 (2007)
Hachimi M., Aghezzaf B.: Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions. J. Math. Anal. Appl. 296, 382–392 (2004)
Hanson M.A.: On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)
Kanniappan P.: Necessary conditions for optimality of nondifferentiable convex multiobjective programming. J. Optim. Theory Appl. 40(2), 167–174 (1983)
Mititelu Şt.: Extensions in invexity theory. J. Adv. Math. Stud. 1(1–2), 63–70 (2008)
Mititelu Şt.: Optimality and duality for invex multi-time control problems with mixed constraints. J. Adv. Math. Stud. 2(1), 25–34 (2009)
Mititelu Şt., Postolache M.: Mond–Weir dualities with Lagrangians for multiobjective fractional and non-fractional variational problems. J. Adv. Math. Stud. 3(1), 41–58 (2010)
Mond B., Husain I.: Sufficient optimality criteria and duality for variational problems with generalized invexity. J. Aust. Math. Soc. Series B. 31, 108–121 (1989)
Nahak, C., Mohapatra, R.N.: Nonsmooth ρ−(η, θ)-invexity in multiobjective programming problems. Optim. Lett. (2010). doi:10.1007/s11590-010-0239-1
Pitea, A., Postolache, M.: Minimization of vectors of curvilinear functionals on the second order jet bundle. Necessary conditions, Optim. Lett. (2011). doi:10.1007/s11590-010-0272-0
Pitea A., Udrişte C., Mititelu Şt.: PDI & PDE-constrained optimization problems with curvilinear functional quotients as objective vectors. Balkan J. Geom. Appl. 14(2), 65–78 (2009)
Pitea A., Udrişte C., Mititelu Şt.: New type dualities in PDI and PDE constrained optimization problems. J. Adv. Math. Stud. 2(1), 81–90 (2009)
Pitea A.: Null Lagrangian forms on 2nd order jet bundles. J. Adv. Math. Stud. 3(1), 73–82 (2010)
Preda V.: On efficiency and duality for multiobjective programs. J. Math. Anal. Appl. 166(2), 365–377 (1992)
Udrişte C., Postolache M.: Atlas of Magnetic Geometric Dynamics. Geometry Balkan Press, Bucharest (2001)
Udrişte C., Dogaru O., Ţevy I.: Null Lagrangian forms and Euler–Lagrange PDEs. J. Adv. Math. Stud. 1(1–2), 143–156 (2008)
Wang S.: Second-order necessary and sufficient conditions in multiobjective programming. Numer. Funct. Anal. Optim. 12(1–2), 237–252 (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pitea, A., Postolache, M. Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions. Optim Lett 6, 1657–1669 (2012). https://doi.org/10.1007/s11590-011-0357-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-011-0357-4