求解Fisher市场均衡问题的内点算法

Fisher 市场均衡是经济学中的经典问题，可以用线性权互补问题来表述。通过调整中心方向向可行点偏移得到新的搜索方向以保证可行性，再利用线性搜索寻找满足邻域条件的最大更新参数来设计求解Fisher市场均衡问题的算法，分析了算法的可行性，证明了算法的迭代复杂度。数值实验结果表明该算法对求解Fisher市场均衡问题是有效的。

An InteriorC-Point Algorithm for Solving Fisher Market Equilibrium Problems

The Fisher market equilibrium is a classic problem in economics, which can be formulated as a linear weight complementarity problem. The new search direction is obtained by adjusting the center direction offset to the feasible point to ensure feasibility, and then the linear search is used to find the maximum update parameter that satisfies the neighborhood conditions to design an algorithm to solve Fisher market equilibrium problems. The feasibility of the algorithm is analyzed, and the iterative complexity of the algorithm is proved. Numerical experimental results show that the algorithm is effective for solving Fisher market equilibrium problems.