math

TLDR Lagrange multipliers is a constrained optimization method Lagrange multipliers restricts solutions to points that are feasible and stationary Key intuitive points: $\nabla{c}$ of our constraint function is normal to the surface.

Optimization Constrained Optimization Optimization is usually bounded. There is a taxonomy of that differ by: type of objective linear non-linear quadratic type of constraints hard soft (optional with penalty) equality inequality number of variables and constraints Solving method slack variables (convert inequality to equality) penalty method with constraints optimal solution or approximation (global or local extrema) convexity differentiability Note that there are similarities and this grouping need not be mutually exclusive