Skip to content
Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

trust-region method

An algorithm that trusts a local quadratic model's advice only within a shrinking or growing radius around the current point.

At an iterate x_k, a trust-region method builds a local quadratic model m_k(p)=f(x_k)+\nabla f(x_k)^\top p+\frac12p^\top B_kp and minimizes it only over steps p with \lVert p\rVert\le r_k, a radius that grows when the model has predicted well and shrinks when it hasn't. Extended to a constrained problem, the same subproblem also enforces the constraints, linearized at x_k, so two different bounds, the ball and the linearized constraint, can each be the one that caps a given step.

Read the full section →
Graph settings

Calculator