# Exercise 3
* Due: 28.1.2016 at noon
* Max points: 8

## General rules
* Send the source code or the written notes of your answers as an attachment to markus.hartikainen@jyu.fi before the due time
* You will get feedback about your answers a week from the due date
* From the second week on, the exercises will be given on the previous Wednesday's lecture

## Exercises

For all of the following problems, we study optimization problem
$$
\begin{align}
\min \qquad & x_1^2+x_2^2 + x_1+2x_2\\
\text{s.t.}\qquad &x_1,x_2\in\mathbb R
\end{align}
$$

1. **(2 points)** Implement a steepest descent algorithm, but do a golden section search to each new search direction. This means that you need to define a single-variable function to determine the step length. Set the length of the interval for doing line search as parameter of the method. Solve above problem using your method.
2. **(3 points)** Plot the steps of the steepest descent algorithm implemented at the class (with fixed step lengths) agains the steps of a steepest descent algorithm that you implemented above. You can choose any starting point you wish, but not the optimum.
3. **(3 points)** Implement the Quasi-Newton method with DFP update as described e.g., at https://en.wikipedia.org/wiki/Davidon%E2%80%93Fletcher%E2%80%93Powell_formula. Solve above problem using this method.


aee1afb51328029114702027da0bbe71700c96f3
ipynb
Jupyter Notebook
Exercise 3.ipynb
maeehart/TIES483
cce5c779aeb0ade5f959a2ed5cca982be5cf2316
CC-BY-3.0
2019-04-26T12:46:14.000Z
2021-11-23T03:38:59.000Z
Exercise 3.ipynb
maeehart/TIES483
cce5c779aeb0ade5f959a2ed5cca982be5cf2316
CC-BY-3.0
Exercise 3.ipynb
maeehart/TIES483
cce5c779aeb0ade5f959a2ed5cca982be5cf2316
CC-BY-3.0
2016-01-08T16:28:11.000Z
2021-04-10T05:18:10.000Z
Qwen/Qwen-72B
1. YES
2. YES

