Lossless convexification of nonconvex MINLP on the UAV path-planning problem

Most unmanned aerial vehicle path-planning problems have been modeled as linear optimal control problems, ie, as mixed-integer linear programming problems. However, most constraints cannot be described accurately in linear form in practical engineering applications. In this paper, the traditional unmanned aerial vehicle path-planning problem is modified as a nonconvex mixed-integer nonlinear programming problem, whose continuous relaxation is a nonconvex programming problem. A lossless convexification method is introduced into the generalized Benders decomposition algorithm framework. Thus, an optimal solution can be obtained without directly solving the nonconvex programming problem. The output of the proposed algorithm has been rigorously proved to be the optimal solution to the original problem. Meanwhile, the simulation results verify the validity of the theoretical analysis and demonstrate the superior efficiency of the proposed algorithm.