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Convex Domains of Given Diameter with Greatest Volume

  • Uwe Klemt
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)

Abstract

In this paper we study the following geometric optimization problem: What are the convex domains of given diameter with greatest volume in the n-dimensional Euclidean space (n ≥ 2)? By using the plane of support of a convex domain we formulate the above mentioned question analytically. This leads to a multidimensional variational problem in parametric form with respect to a class of state functions and associated control vectors of Grassmann coordinates fulfilling certain state restrictions, control restrictions and boundary conditions. In order to prove the conjecture that circle and ball, respectively, are domains solving the problem we apply a generalized duality theory in the sense of R. Klötzler. On the basis of this theory first-order necessary conditions and second-order sufficiency conditions for an auxiliary finite-dimensional parametric optimization problem are verified.

Keywords

Convex Domain Maple Versus Weak Local Minimizer Strong Local Minimizer Control Constraint State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Uwe Klemt
    • 1
  1. 1.Lehrstuhl OptimierungBTU CottbusCottbusGermany

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