Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving exactly/deterministically such instances is to cast them as a linear programming instances. Inversely, this paper introduces a self-concordant perceptron algorithm which tackles directly strict linear feasibility with interior point paradigm. This algorithm has the same worse times complexity than state of the art linear programming algorithms but it complexity can be characterized more precisely eventually proving that it binary complexity is low on a sub-family of linear feasibility.

翻译：严格线性可行性或线性分离问题通常通过高效的近似/随机算法处理（这些算法在期望情况下甚至能以次线性时间运行）。然而，当前精确/确定性求解此类实例的最先进方法仍将其转化为线性规划问题。与之相反，本文提出了一种基于内点法范式的自洽感知器算法，直接处理严格线性可行性问题。该算法的最坏时间复杂度与当前最先进的线性规划算法相同，但其复杂度可被更精确地刻画，最终证明该算法在特定线性可行性子族上具有较低的二进制复杂度。