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Extensions of the Evans-Gould Stability Theorems for Mathematical Programs

Author

Listed:
  • Harvey J. Greenberg

    (Southern Methodist University, Dallas, Texas)

  • William P. Pierskalla

    (Northwestern University, Evanston, Illinois)

Abstract

This paper extends the results of Evans and Gould for stability in mathematical programming. In particular, it shows that their conditions apply to functional perturbation, to equality constraints, and to policy stability under certain conditions. Further, it shows that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability. Finally, some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings.

Suggested Citation

  • Harvey J. Greenberg & William P. Pierskalla, 1972. "Extensions of the Evans-Gould Stability Theorems for Mathematical Programs," Operations Research, INFORMS, vol. 20(1), pages 143-153, February.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:1:p:143-153
    DOI: 10.1287/opre.20.1.143
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    Cited by:

    1. E. Muselli, 2000. "Upper and Lower Semicontinuity for Set-Valued Mappings Involving Constraints," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 527-550, September.
    2. Giorgio & Cesare, 2018. "A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions," DEM Working Papers Series 159, University of Pavia, Department of Economics and Management.

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