×

Duality for nonsmooth continuous-time problems of vector optimization. (English) Zbl 1194.90089

Summary: We consider a nonsmooth vector optimization continuous-time problem. We establish weak and strong duality theorems under generalized convexity assumptions.

MSC:

90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
Full Text: DOI

References:

[1] Bellman, R.: Bottleneck problems and dynamic programming. Proc. Natl. Acad. Sci. USA 39, 947–951 (1953) · Zbl 0053.27903 · doi:10.1073/pnas.39.9.947
[2] Hanson, M.A.: Duality for a class of infinite programming problems. SIAM J. Appl. Math. 16, 318–323 (1986) · Zbl 0171.40702 · doi:10.1137/0116025
[3] Farr, W.H., Hanson, M.A.: Continuous-time programming with nonlinear constraints. J. Math. Anal. Appl. 45, 96–115 (1974) · Zbl 0299.90025 · doi:10.1016/0022-247X(74)90124-3
[4] Reiland, T.W., Hanson, M.A.: Generalized Kuhn-Tucker conditions and duality for continuous for nonlinear programming problems. J. Math. Anal. Appl. 74, 578–598 (1980) · Zbl 0437.49036 · doi:10.1016/0022-247X(80)90149-3
[5] Reiland, T.W.: Optimality conditions and duality in continuous programming I. Convex programs and a theorem of alternative. J. Math. Anal. Appl. 77, 329–343 (1980) · Zbl 0459.90044 · doi:10.1016/0022-247X(80)90230-9
[6] Zalmai, G.J.: Proper efficiency conditions and duality models for a class of nonsmooth continuous-time multiobjective fractional programming problems. Southeast Asian Bull. Math. 27, 155–186 (2003) · Zbl 1137.90664
[7] Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983) · Zbl 0582.49001
[8] Clarke, F.H., Ledyaev, Y.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Graduate Texts in Mathematics, vol. 178. Springer, New York (1998) · Zbl 1047.49500
[9] Chankong, V., Haimes, Y.: Multiobjective Decision Making; Theory and Methodology. North-Holland, New York (1983) · Zbl 0622.90002
[10] Nobakhtian, S.: Optimality criteria for nonsmooth multiobjective continuous-time problems. J. Optim. Theory Appl. (to appear) · Zbl 1194.90088
[11] Zalmai, G.J.: Optimality conditions and Lagrangian duality in continuous-time nonlinear programming. J. Math. Anal. Appl. 109, 426–452 (1985) · Zbl 0589.90069 · doi:10.1016/0022-247X(85)90160-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.