EXPLICIT SOLUTION OF THE LP-MODEL OF THE NEURAL NETWORK LEARNING PROBLEM

Abstract

In [2] the neural network learning problem was formulated as the following LP-problem:

Find \(x_j \geq 0,\ j=1,\ldots,n+1\) which satisfy the \(n^2+1\) constraints:

\[
x_i-a_{si}x_s+h_ix_{n+1}\geq 0,
\qquad i\ne s,\quad i,s=1,\ldots,n
\]

\[
x_i-x_{n+1}\geq 0,
\qquad i=1,\ldots,n
\]

\[
x_1+x_2+\cdots+x_n=1
\]

and maximize the linear form \(z=x_{n+1}\);
all the \(a_{si}\), \(h_i\), \(0\leq a_{si}<h_i\leq 1\) are assumed to be known. Then, the feasible bases to the dual problem in standard form were discussed.

Now, we consider directly the above stated LP-problem and characterize the extreme points of the set of feasible solutions.