A Method of Nonparametric Estimation of Unique Unknown Objective Function Using Sets of Constraint Condition and Corresponding Optimal Solution Data : The Case of Concave Programming with Linear Inequalities Constraint

In this paper, we present a nonparametric linear programming estimation method of unique unknown objective function in concave programming with linear inequalities constraint, using sets of constraint condition and corresponding optimal solution data. We also present a linear programming method of maximizing the estimated objective function under new constraint. A case study of simple experimental problem proves the usefulness of our methods. Finally, we show the implications of this paper and problems to be solved in the future