Warmstart

Warmstart is a technique for initializing an iterative problem solver with a starting point informed by a previously solved or related problem. The idea is to reuse information from past runs to accelerate convergence, reduce computation time, and improve robustness. In some contexts, warmstarts are contrasted with cold starts (no prior information) and, in certain communities, with hot starts (a particularly strong or feasible initial solution).

In numerical optimization, a warm start uses a solution, basis, or dual variables from a prior solve as the initial point for the current run. This is beneficial when successive problem instances are similar, as the starting point is often near the current optimum. For linear and quadratic programming, reusing the previous optimal basis or a feasible point can substantially reduce iterations. In mixed-integer programming, providing an incumbent solution or a partial basis during solve can act as a warmstart that guides the search more efficiently.

In model predictive control and other dynamic optimization problems, warmstarting is a standard practice: the optimizer is initialized with the previous time step’s solution, since the problem changes gradually over time. In machine learning, warm starts can refer to initializing models with pretrained weights or leveraging prior optimization trajectories to speed up subsequent training or hyperparameter searches.

Benefits of warmstarting include faster convergence, lower computational cost, and better performance in real-time or rapidly evolving settings. Limitations include the risk that a poor or outdated starting point impedes progress, possible constraint infeasibility, and the need to adapt starting information when problem data changes significantly. Good practices involve feasibility checks, projection or correction of the initial point if needed, and updating the starting point as data evolves.