Convex programs for solving (3.1)–(3.4a),(3.5)

  • Kurt Marti
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 299)


For a given n-vector x let (y,π) denote a solution of (3.1)–(3.3). According to section 2.7 for the transition probability measures Kj, j ∈ R, we have that
$${K^j} = \sum\limits_{i \in R} {{\beta _{ij}}{\varepsilon _{{Z^i}}} = \sum\limits_{i \in S} {{{\tilde \beta }_{ij}}{\varepsilon _{{z^i}}}} } $$
with \(\sum\limits_{i \in R} {{\beta _{ij}} = \sum\limits_{i \in S} {{{\tilde \beta }_{ij}} = 1,} } \) where \({\beta _{ij}} = \frac{{{\alpha _i}{\pi _{ij}}}}{{{\alpha _j}}},\) i, j ∈ R, and \({\tilde \beta _{ij}} = \frac{{{{\tilde \alpha }_i}{\tau _{ij}}}}{{{\alpha _j}}},{\tilde \alpha _i} = \sum\limits_{{z^t} = {z^i}} {{\alpha _t},{\tau _{ij}} = {\tau _{ij}}\left( \pi \right) = \frac{1}{{{{\tilde \alpha }_i}}}} \sum\limits_{{z^t} = {z^i}} {{\alpha _t}{\pi _{tj}},i \in S} ,j \in R\), see (13); let T=T (π) = (τij).


Convex Subset Entropy Maximization Variance Maximization Stochastic Program Convex Program 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Kurt Marti
    • 1
  1. 1.Fakultät für Luft- und RaumfahrttechnikUniversität der Bundeswehr MünchenNeubibergGermany

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