Stability of the Feasible Set Mapping in Convex Semi-Infinite Programming

  • Marco A. López
  • Virginia N. Vera de Serio
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 57)


In this paper we approach the stability analysis of the feasible set mapping in convex semi-infinite programming for an arbitrary index set. More precisely, we establish its closedness and study the semicontinuity, in the sense of Berge, of this multivalued mapping- A certain metric is proposed in order to measure the distance between nominal and perturbed problems. Since we do not require any structure to the index set, our results cover the ordinary convex programming problem.


Multivalued Mapping SIAM Journal Metrizable Space Linear Inequality System Convex System 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Canovas, M. Lopez, J. Parra and M. Todorov. Stability and well-posedness in linear semi-infinite programming, SIAM Journal on Optimization, 10:82–98, 1999.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    M. Goberna and M. Lopez. Topological stability of linear semi-infinite inequality systems, Journal of Optimization Theory and its Applications, 89:227–236, 1996.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    M. Goberna and M. Lopez. Linear Semi-Infinite Optimization, Wiley, 1998.MATHGoogle Scholar
  4. [4]
    M. Goberna, M. Lopez and M. Todorov. Stability theory for linear inequality systems, SIAM Journal on Matrix Analysis and Applications, 17:730–743, 1996.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    M. Goberna, M. López and M. Todorov. Stability theory for linear inequality systems II: Upper semicontinuity of the solution set mapping, SI AM Journal on Optimization, 7:1138–1151, 1997.MATHCrossRefGoogle Scholar
  6. [6]
    W. Li, C. Nahak and I. Singer. Constraint qualifications for semi-infinite systems of convex inequalities, SIAM Journal on Optimization, 11:31–52, 2000.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    S. Robinson. Stability theory for systems of inequalities. Part I: Linear systems, SIAM Journal on Numerical Analysis, 12:754–769, 1975.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    R. Rockafellar. Convex Analysis, Princeton University Press, 1970.MATHGoogle Scholar
  9. [9]
    R. Rockafellar and R. B. Wets. Variational Analysis, Springer-Verlag, 1998.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Marco A. López
    • 1
  • Virginia N. Vera de Serio
    • 2
  1. 1.Department of Statistics arid Operations Research, Faculty of SciencesAlicante UniversityAlicanteSpain
  2. 2.Faculty of Economic SciencesUniversidad Nacional de CuyoMendozaArgentina

Personalised recommendations