# 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)

## Abstract

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
$${K^j} = \sum\limits_{i \in R} {{\beta _{ij}}{\varepsilon _{{Z^i}}} = \sum\limits_{i \in S} {{{\tilde \beta }_{ij}}{\varepsilon _{{z^i}}}} }$$
(15)
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).

Entropy