Semi-Infinite Programming and Applications

  • S.-Å. Gustafson
  • K. O. Kortanek


An important list of topics in the physical and social sciences involves continuum concepts and modelling with infinite sets of inequalities in a finite number of variables. Topics include: engineering design, variational inequalities and saddle value problems, nonlinear parabolic and bang-bang control, experimental regression design and the theory of moments, continuous linear programming, geometric programming, sequential decision theory, and fuzzy set theory. As an optimization involving only finitely many variables, semi-infinite programming can be studied with various reductions to finiteness, such as finite subsystems of the infinite inequality system or finite probability measures.

This survey develops the theme of finiteness in three main directions: (1) a duality theory emphasizing a perfect duality and classification analogous to finite linear programming, (2) a numerical treatment emphasizing discretizations, cutting plane methods, and nonlinear systems of duality equations, and (3) separably-infinite programming emphasizing its uniextremal duality as an equivalent to saddle value, biextremal duality. The focus throughout is on the fruitful interaction between continuum concepts and a variety of finite constructs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • S.-Å. Gustafson
    • 1
  • K. O. Kortanek
    • 2
  1. 1.Department of Numerical Analysis and Computing ScienceRoyal Institute of TechnologyStockholm 70Sweden
  2. 2.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA

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