Customized First Order Convex Optimization Algorithm for Powered-Descent Guidance

This paper introduces the extrapolated proportional integral projected gradient (ePIPG) method, a newly developed first-order method, for second-order cone programming problems (SOCP), and its customized implementation to solve the 3-DoF powered-descent guidence problem. The ePIPG solvers parse the problem parametets automatically to fully utilize the problem sparse structure. In addition, different from the classic interior-point method, being a first-order method, ePIPG only relies on simple algebra operations, for example, projection onto convex sets, multiplication of matrix and vector and vectors addition. The numerical experiment shows that the customized ePIPG solver is significantly faster than ECOS and GUROBI, two advanced convex optimization solvers, thus is a potential method for future rocket landing missions.