In view of the extended formulations (EFs) developments (e.g. "Fiorini, S., S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf [2015]. Exponential Lower Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM 62:2"), we focus in this paper on the question of whether it is possible to model an NP-Complete problem as a polynomial-sized linear program. For the sake of simplicity of exposition, the discussions are focused on the TSP. We show that a finding that there exists no polynomial-sized extended formulation of "the TSP polytope" does not (necessarily) imply that it is "impossible" for a polynomial-sized linear program to solve the TSP optimization problem. We show that under appropriate conditions the TSP optimization problem can be solved without recourse to the traditional city-to-city ("travel leg") variables, thereby side-stepping/"escaping from" "the TSP polytope" and hence, the barriers. Some illustrative examples are discussed.

翻译：鉴于扩展公式（EF）领域的发展（例如“Fiorini, S., S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf [2015]. 组合优化中多面体的指数下界. 《美国计算机学会期刊》62:2”），本文聚焦于能否将NP完全问题建模为多项式规模线性规划的问题。为简化阐述，讨论围绕旅行商问题（TSP）展开。我们证明：发现“TSP多面体”不存在多项式规模扩展公式这一结果，并不（必然）意味着“不可能”存在一个多项式规模线性规划来求解TSP优化问题。我们展示在适当条件下，TSP优化问题可以通过摆脱传统的城市间（“旅行路段”）变量进行求解，从而绕过/“避开”“TSP多面体”，进而克服相关障碍。文中讨论了若干示例加以说明。