Optimality conditions and duality for a class of continuous-time programming problems with nonlinear operator equality and inequality constraints

作者: G.J Zalmai

DOI: 10.1016/0022-247X(90)90216-3

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摘要: Abstract Using a minmax approach, we establish saddle point optimality conditions and Lagrangian duality relations under generalized convexity hypotheses for class of continuous-time programming problems with nonlinear operator equality inequality constraints. We also discuss the implications these results differentiable problems.

参考文章(24)
Aleksandr Davidovich Ioffe, Vladimir M. Tikhomirov, Theory of extremal problems ,(1979)
Christoph Witzgall, Josef Stoer, Convexity and Optimization in Finite Dimensions I ,(1970)
Thomas W Reiland, Optimality conditions and duality in continuous programming I. Convex programs and a theorem of the alternative Journal of Mathematical Analysis and Applications. ,vol. 77, pp. 297- 325 ,(1980) , 10.1016/0022-247X(80)90278-4
G.J Zalmai, Optimality conditions and Lagrangian duality in continuous-time nonlinear programming Journal of Mathematical Analysis and Applications. ,vol. 109, pp. 426- 452 ,(1985) , 10.1016/0022-247X(85)90160-X
Maurice Sion, On general minimax theorems Pacific Journal of Mathematics. ,vol. 8, pp. 171- 176 ,(1958) , 10.2140/PJM.1958.8.171
Thomas W. Reiland, Lagrangian duality for a class of infinite programming problems Numerical Functional Analysis and Optimization. ,vol. 2, pp. 507- 530 ,(1980) , 10.1080/01630568008816073
William H Farr, Morgan A Hanson, Continuous time programming with nonlinear time-delayed constraints☆ Journal of Mathematical Analysis and Applications. ,vol. 46, pp. 41- 61 ,(1974) , 10.1016/0022-247X(74)90280-7
Josef Stoer, Duality in nonlinear programming and the minimax theorem Numerische Mathematik. ,vol. 5, pp. 371- 379 ,(1963) , 10.1007/BF01385903
J. Ponstein, Multiplier Functions in Optimal Control Siam Journal on Control. ,vol. 6, pp. 648- 658 ,(1968) , 10.1137/0306042
C. H. SCOTT, T. E. JEFFERSON, Duality for convex functionals: specific cases International Journal of Systems Science. ,vol. 8, pp. 1313- 1320 ,(1977) , 10.1080/00207727708942123