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Memory Cards — Chapter 14
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Trust region
Trust-region methods restrict the step to where the model is reliable.
Line search
Line search chooses a step length that gives sufficient decrease and protects global convergence.
KKT
KKT conditions summarize constrained optimality: stationarity, feasibility, dual feasibility, and complementarity.
Optimization problem
Optimization seeks a minimizer subject to assumptions, constraints, and practical stopping rules.
Gradient
The gradient is the first-order stationarity object; \(\nabla f=0\) is necessary for unconstrained smooth minima.
Hessian
The Hessian describes curvature and guides Newton-type steps.