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）的发展（例如“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”），本文聚焦于一个核心问题：是否可能将NP完全问题建模为一个多项式规模的线性规划。为简化阐述，讨论将围绕旅行商问题（TSP）展开。我们表明：发现“TSP多面体”不存在多项式规模扩展公式，并不（必然）意味着不可能通过多项式规模线性规划求解TSP优化问题。我们证明，在适当条件下，无需依赖传统的城市间（“旅行段”）变量即可求解TSP优化问题，从而规避/“绕开”“TSP多面体”及其相关障碍。文中还讨论了一些示例。