Warm-Start of Interior-Point Methods Applied to Sequential Convex Programming

Sequential convex programming (SCP) is an iterative technique that solves nonconvex optimization problems by considering a sequence of convex subproblems whose solutions eventually converge, under certain conditions, to the solution of the original problem. The most common convex solvers divide in interior-point, first-order, and active-set methods. In particular, the former have shown good performance. Even though SCP is quite efficient in terms of required computational time with respect to standard nonlinear optimization solvers, its potential is still not completely exploited when interior-point convex solvers are used as no information on the solution of a previous convex subproblem is used to construct the initial guess for the strictly-related following one. This is because interior-point methods are notoriously difficult to warm-start. In this paper, a technique to warm-start interior-point methods that solve secondorder cone programs (SOCP) is developed and integrated within the sequential convex programming. The strategy can be used independently of the specific problem as long as it is expressed as a standard SOCP. The low-thrust space trajectory optimization problem is considered to assess the efficacy of the proposed strategy through extensive numerical simulations. It is shown that the warm-start algorithm outperforms the standard algorithm in terms of computational time and overall convergence when the widely-used solver ECOS is used.