# Review Questions for Optimization

- What are the necessary and sufficient conditions for a point to be a local minimum in one dimension?
- What are the necessary and sufficient conditions for a point to be a local minimum in \(n\) dimensions?
- How do you classify extrema as minima, maxima, or saddle points?
- What is the difference between a local and a global minimum?
- What does it mean for a function to be unimodal?
- What special attribute does a function need to have for golden section search to find a minimum?
- Run one iteration of golden section search.
- Calculate the gradient of a function (function has many inputs, one output).
- Calculate the Jacobian of a function (function has many inputs, many outputs).
- Calculate the Hessian of a function.
- Find the search direction in steepest/gradient descent.
- Why must you perform a line search each step of gradient descent?
- Run one step of Newton's method in one dimension.
- Run one step of Newton's method in \(n\) dimensions.
- When does Newton's method fail to converge to a minimum?
- What operations do you need to perform each iteration of golden section search?
- What operations do you need to perform each iteration of Newton's method in one dimension?
- What operations do you need to perform each iteration of Newton's method in \(n\) dimensions?
- What is the convergence rate of Newton's method?