# Exercise 6
* Due: 18.2.2016 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

1. **2 points** Solve optimization problem
$$
\begin{align}
\min \quad &\log(x_1^2+1)+x_2^4+x_1x_3\\
\text{s.t. }\quad &x_1^3-x_2^2\geq 1\\
& x_1,x_3\geq 0, \ x_2\in\mathbb R
\end{align}
$$
using any method that you have available.
2. **2 points** Study multiobjective optimization problem
$$
\begin{align}
\min & \{\|x-(1,0)\|^2,\|x-(0,1)\|^2\}\\
\text{s.t. }&x\in \mathbb R^2.
\end{align}
$$
Chacterize algebraicly the full set of Pareto optimal solutions.
3. **2 points** Calculate the ideal and nadir vectors for the problem of 2. You can use any methods available.
4. **2 points** Try to generate a representative set of Pareto optimal solutions using the weighting method for the problem of 2. Compare this set to the set of Pareto optimal solutions from 2. What do you notice?

c399e59ea22a17dd6e9b16865cc6f79d74d756af
ipynb
Jupyter Notebook
Exercise 6.ipynb
maeehart/TIES483
cce5c779aeb0ade5f959a2ed5cca982be5cf2316
CC-BY-3.0
2019-04-26T12:46:14.000Z
2021-11-23T03:38:59.000Z
Exercise 6.ipynb
maeehart/TIES483
cce5c779aeb0ade5f959a2ed5cca982be5cf2316
CC-BY-3.0
Exercise 6.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

