Adjusting an Objective Function to a Given Optimal Solution in Linear and Linear-fractional Programming

We consider a special problem in the context of linear and linear-fractional programming: Given an objective function on a bounded feasible set S, the optimal vertex x*, and a neighboring vertex x, adjust the objective function to make x the new optimum. Such a problem emerges in expert systems, where the system’s objective function “learns” to recognize “correct” optima provided by an expert.