interior-point method
A method that follows the central path using one cheap Newton step per parameter value, instead of fully re-solving each barrier subproblem.
A primal-dual interior-point method applies Newton's method directly to the perturbed KKT system, stationarity plus the perturbed complementary slackness condition \lambda\,g(x)=-\mu, updating the primal variable x and the implied multiplier \lambda together in one linear step, then shrinking \mu and repeating. This tracks the central path with far less work per step than fully minimizing a fresh barrier subproblem at every \mu.
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