An efficient optimization algorithm for quadratic programming problem and its applications to mobile robot path planning

[摘要] The quadratic programming problem has broad applications in mobile robot path planning. This article presents an efficient optimization algorithm for globally solving the quadratic programming problem. By utilizing the convexity of univariate quadratic functions, we construct the linear relaxation programming problem of the quadratic programming problem, which can be embedded within a branch-and-bound structure without introducing new variables and constraints. In addition, a new pruning technique is inserted into the branch-and-bound framework for improving the speed of the algorithm. The global convergence of the proposed algorithm is proved. Compared with some known algorithms, numerical experiment not only demonstrates the higher computational efficiency of the proposed algorithm but also proves that the proposed algorithm is an efficient approach to solve the problems of path planning for the mobile robot.

[学科分类] 自动化工程

[关键词] Quadratic programming problem;global optimization;linear relaxation programming;pruning technique;branch-;-bound optimization algorithm;path planning