Review and coding practice with classic approximation and optimization methods, root computation, derivatives, limits computation using python and symbolic library sympy.
- Finding collection of extremas in a one time differentiable function using sympy. finding_extremas
- First-order approximation to find closest root, context must satisfy Intermediate Value Theorem.
- Works for f(x) and g(x) since both have solutions near initialization point x0.
- Optimization method that involve second-order approximations of the objective function using 1st and 2nd derivaties for univariable problems, and gradient and Hessian for multivariable problems.
- Univariable problems: doesn't work for f(x) since it is a non-convex function, works for g(x) that is convex in interval [0,1].