EXPLICIT SOLUTION OF THE LP-MODEL OF THE NEURAL NETWORK LEARNING PROBLEM - Karčicka, Dimitra; Jovančevski, Gjorgji (Matematichki Bilten, 1998)
In [2] the neural network learning problem was formulated as the following LP-problem: Find \(x_j ≥ 0, j=1,…,n+1\) which satisfy the \(n^2+1\) constraints: \[ x_i-a_six_s+h_ix_n+1≥ 0, i e s,i,s=1,…,n \] \[ x_i-x_n+1≥ 0, i=1,…,n \] \[ x_1+x_2+…+x_n=1 \] and maximize the linear form \(z=x_n+1\); all the \(a_si\), \(h_i\), \(0≤ a_si<h_i≤ 1\) 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.