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Original Articles

Perturbed minimization, with constraints adjoined or deleted

Pages 23-36 | Received 01 Nov 1980, Published online: 27 Jun 2007

References

  • Alt , W. 1980 . Lipschitzian perturbations of infinite optimization problems . Proceedings of the Second Symposium on Mathematical Programming with Data Perturbations . 1980 , Washington. to appear
  • Auslender , A. 1979 . Differential stability in nonconvex and nondifferentiable mathematical programming . Math. Programming Study , 10 : 29 – 41 .
  • Ben-Isreal , A. , Ben-Tal , A. and Zlobec , S. Optimality conditions in convex programming . Survey of Mathematical Programming Proceedings of 9th. International Symposium on Mathematical Programming . 1976 , Budapest. Edited by: Prekopa , A. Vol. 1 , pp. 153 – 170 . Amsterdam : North-Holland .
  • Graven , B.D. 1977 . Lagrangean conditions and quasiduality . Bull. Austral. Math. Soc , 16 : 325 – 339 .
  • Graven , B.D. 1978 . Mathematical Programming and Control Theory , London : Chapman and Hall .
  • Craven , B.D. 1980 . Implicit function theorems and LagrangeAN multipliers . Numerical Functional Analysis and Optimization , 2 ( 6 ) : 473 – 486 .
  • Dolecki , S. 1978 . Semicontinuity in constrained optimization, II . Metric spaces. Contr. Cybernet , 7 ( 6 ) : 5 – 16 .
  • Dolecki , S. and Rouswicz , S. 1979 . Metric characterizations of upper semicontinuity . J. Math. Anal. Appl , 69 ( 6 ) : 146 – 152 .
  • Evans , J.P. and Gould , F.J. 1970 . Stability in nonlinear programming . Opns. Res , 18 ( 6 ) : 107 – 118 .
  • Fiacco , A.V. and Hutzleb , W.P. April 1979 . Extensions of the Gauvin-Toixe optimal value differential stability results to general mathematical programs , April , George Washington University . Institute for Management Science and Administration, Report T-393
  • Gauvin , J. and Tolle , J.M. 1977 . Differential stability in nonlinear programming . SIAM J. Control Optim , 15 April : 294 – 311 .
  • Greenberg , H.J. and Pierskalla , W.P. 1972 . Extensions of the Evans-Gould stability theorems for mathematical programs . Opns. Res , 20 April : 143 – 153 .
  • Greenberg , H.J. and Pierskalla , W.P. 1975 . Stability theorems for infinitely constrained mathematical programs . J. Optim. Theor. Appl , 16 April : 409 – 438 .
  • Kaneko , H. and Ruckle , M.H. 1980 . SCHAUDER decompositions, approximations and control problems . SIAM J. Control Optim , 18 April : 381 – 390 .
  • Kummer , B. 1977 . Globale Stabilität quadratischer Optimierungsprobleme . Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe , 26 ( 5 ) April : 565 – 569 .
  • Kummer , B. 1977 . Global stability of optimization problems. Math. Operationsforsch . Statist. Ser. Optimization , 8 ( 3 ) April : 367 – 383 .
  • Kummer , B. 1978 . “ Stetigkeitsverhalten von Punkt-Menge-Abbildungen in der Mathema-tischen Optimierung ” . In Fortschritte in der mathematischen Optimierung , Vol. 15 , 76 – 86 . Berlin : Humboldt Univ . Tagung, Humboldt Univ., Berlin, (1978)
  • Kummer , B. 1979 . A note on the continuity of the solution set of special dual optimization problems . Math, Programming Study , 10 : 110 – 114 .
  • Lempio , F. and Maurer , H. 1980 . “ Differential stability in infinite-dimensional nonlinear programming ” . In Appl. Math. Optim Vol. 6 , 139 – 152 .
  • Maurer , H. Jan 1977 . “ A sensitivity result for infinite nonlinear programming problems, I ” . In Theory. Math. Institut Wiirzburg Vol. 21 , Jan , Preprint
  • Maurer , H. 1977 . Zur Störungstheorie in den infiniter Optimierung . Zeits. angew. Math. Mech , 57 Jan : 340 – 341 .
  • Maueer , H. 1979 . Differential stability in optimal control problems . Appl. Math, Optim , 5 Jan : 283 – 295 .
  • Robinson , S.M. 1976 . Stability theory for systems of inequalities; Part 1:differentiabie Nonlinear systems . SIAM J. Numer. Anal , 13 Jan : 497 – 513 .
  • Zlobec , S. and Ben-Israel , A. 1978 . Perturbed Convex Programs; continuity of optimal Solutions and optimal values . Operations Research Verfahren , 31 Jan : 737 – 749 .

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