Mathematical Programming

, Volume 53, Issue 1–3, pp 267–277 | Cite as

A note on d-stability of convex programs and limiting Lagrangians

  • C. Zălinescu


In this paper we give a criterion for d-stability of convex programs and a perturbation result which subsume and generalize some recent results in semi-infinite programming and limiting Lagrangians.

Key words

d-stability convex optimization perturbations recession cone recession function 


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  1. [1]
    V. Barbu and Th. Precupanu,Convexity and Optimization in Banach Spaces (Editura Academiei Bucureşti, Reidel, Dordrecht-Boston-Lancaster, 1986).Google Scholar
  2. [2]
    C.E. Blair, R.J. Duffin and R.G. Jeroslow, “A limiting infisup theorem,”Journal of Optimization Theory and Applications 37 (1982) 163–175.Google Scholar
  3. [3]
    J.M. Borwein, “A note on perfect duality and limiting Lagrangians,”Mathematical Programming 18 (1980) 330–337.Google Scholar
  4. [4]
    J.M. Borwein, “The limiting Lagrangian as a consequence of Helly's theorem,”Journal of Optimization Theory and Applications 33 (1981) 497–513.Google Scholar
  5. [5]
    J.M. Borwein, “Adjoint process duality,”Mathematics of Operations Research 8 (1983) 403–434.Google Scholar
  6. [6]
    T. Ekeland and R. Temam,Analyse Convexe et Problèmes Variationels (Dunod, Gauthier-Villars, Paris, 1974).Google Scholar
  7. [7]
    R.B. Holmes,Geometric Functional Analysis and its Applications (Springer, Berlin, 1975).Google Scholar
  8. [8]
    R.G. Jeroslaw, “A limiting Lagrangian for infinitely constrained convex optimization in ℝn,”Journal of Optimization Theory and Applications 33 (1981) 479–495.Google Scholar
  9. [9]
    D.F. Karney, “Duality theorem for semi-infinite convex programs and their finite subprograms,”Mathematical Programming 27 (1983) 75–82.Google Scholar
  10. [10]
    D.F. Karney and T.D. Morley, “Limiting Lagrangians: A primal approach,”Journal of Optimization Theory and Applications 48 (1986) 163–174.Google Scholar
  11. [11]
    P.-J. Laurent,Approximation et optimisation (Herman, Paris, 1972).Google Scholar
  12. [12]
    L. McLinden, “Quasistable parametric optimization without compact level sets,” Technical Summary Report No. 2708, Mathematics Research Center, University of Wisconsin-Madison (Madison, WI, 1984).Google Scholar
  13. [13]
    J.-Ch. Pomerol, “Contribution à la programmation mathématique: Existence de multiplicateurs de Lagrange et stabilité,” Thesis, P. and M. Curie University (Paris, 1980).Google Scholar
  14. [14]
    J.-Ch. Pomerol, “A note on limiting infisup theorems,”Mathematical Programming 30 (1984) 238–241.Google Scholar
  15. [15]
    T. Precupanu, Closedness conditions for the optimality of a family of non-convex optimization problems,Mathematische Operationsforschung und Statistik Series Optimization 15 (1984) 339–346.Google Scholar
  16. [16]
    R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, NJ, 1970).Google Scholar
  17. [17]
    R.T. Rockafellar,Conjugate Duality and Optimization. Regional Conference Series in Applied Mathematics No. 16 (SIAM, Philadelphia, PA, 1974).Google Scholar
  18. [18]
    C. Zălinescu, “On an abstract control problem,”Numerical Functional Analysis and Optimization 2 (1980) 531–542.Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1992

Authors and Affiliations

  • C. Zălinescu
    • 1
  1. 1.Faculty of MathematicsUniversity of IaşiIaşiRomania

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