A Comprehensive Survey of Linear Semi-Infinite Optimization Theory

  • Miguel A. Goberna
  • Marco A. López
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 25)


This paper reviews the lineax semi-infinite optimization theory as well as its main foundations, namely, the theory of linear semi-infinite systems. The first part is devoted to existence theorems and geometrical properties of the solution set of a linear semi-infinite system. The second part concerns optimality conditions, geometrical properties of the optimal set and duality theory. Finally, the third part analyzes the well-posedness of the linear semi-infinite programming problem and the stability (or continuity properties) of the feasible set, the optimal set and the optimal value mappings when all the data are perturbed.


Duality Theorem Inconsistent System Linear Inequality System Conical Convex Hull Strong Uniqueness Property 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Miguel A. Goberna
    • 1
  • Marco A. López
    • 1
  1. 1.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain

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