warmstarting

Warmstarting is a technique used in numerical optimization and related computational methods in which a solver is given an initial guess for the decision variables, and sometimes dual variables or auxiliary quantities, that is derived from a previous solution or a heuristic. The goal is to exploit similarities between consecutive problems to accelerate convergence and reduce computational effort.

In practice, warmstarting often involves reusing information from a prior solve. This can include the previous primal solution, dual variables, an active set, a factorization of a system matrix, or a preconditioner. It is commonly applied in iterative methods, linear and quadratic programming, and in interior-point methods. A prominent example is model predictive control, where a new quadratic program is solved at each control step with the previous step’s solution as the starting point, and sometimes with updated constraints reflecting the latest measurements.

Benefits of warmstarting include faster convergence, reduced iteration counts, and lower online computation time, which are especially important in real-time or online settings, large-scale problems, and sequential problem families. It can improve robustness when problem instances change gradually.

Cautions include the risk that a previous solution is a poor or infeasible starting point for the new problem, which can slow convergence or lead to solver instability. Therefore, warmstarting often requires safeguards such as feasibility restoration steps, checks for significant problem changes, or occasional cold restarts. In nonconvex problems, warmstarting may bias toward local optima.