An Optimal Equilibrium Solution Approach for Bi-level Nonlinear Programming Problem Using Lingo Software

In order to solve a bi-level nonlinear programming problem (BL-NLP) satisfying the certain convexity conditions, a new method is proposed in this paper. This method uses the concepts called optimal equilibrium solution and optimal equilibrium value for getting the Pareto optimal solution of BL-NLP. It has two main features. First, within lower-level decision-makers (LDM) [or within higher-level decision-makers (HDM)], for any fixed variable of HDM (or for any fixed variable of LDM), the optimal equilibrium solution is a Pareto optimal solution within LDM (or within HDM), and the optimal equilibrium value is a minimal uniform concession of all the decision-makers within LDM (or HDM) relative to their individual optimal objectives. Thus, the optimal equilibrium solution is an impartial solution within LDM (or HDM).