2023/12/04 by Shcherbak, Denys, Arnqvist, Natalya Pya
#Algebraic Geometry (math.AG) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2312.01775
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the same time, it ensures that previously fulfilled constraints are not breached during this process. The method is based on geometrical properties of n-dimensional space and can be used on any type of linear constraints (>, =, ≥), moreover it can be used when the feasible region is non-full-dimensional.