A Non-Differential Approach for Solving Tri-Level Programming Problems

I. Introduction Multi-level programming is a powerful technique for solving hierarchical decision-making problems.Multi-level optimization plays an important role in engineering design, management, and decision making in general. Ultimately, a designer or decision maker needs to make tradeoffs between disparate and conflicting design objectives. The field of multi-level optimization defines the art and science of making such decisions. The prevailing approach for address this decision-making task is to solve an optimization problem, which yields a candidate solution. A tri-level programming problem (TLPP) is a special case of multi-level programming problem (MLPP). Multi-level programming problem can be defined as a p-person, non-zero sum game with perfect information in which each player moves sequentially from top to bottom. This problem is a nested hierarchical structure. When