Homework 11

CHE 116: Numerical Methods and Statistics

4/11/2019


1. Conceptual Questions

  1. What is the difference between a bound and a constraint?
  2. What must you consider before choosing a method for minimization?
  3. Give an example of a non-convex problem you might see in chemical engineering.

2. Optimization Problems

Solve and plot the following expressions using python. Plot a red dot at your solution.

  1. Find all roots of this expression:
$$ \frac{(x−4)^4}{8}+ \frac{(x−2)^2}{2} - 4 $$
  1. Find the minimum of this expression with $r$ bounded to be $[0.9,3]$
$$ 4\left[\frac{1}{r^8} - \frac{1}{r^4}\right] $$
  1. Solve $e^{x / 4} = x$

  2. You do not need to plot this problem. Solve the following system of equations and report your answer.

$$ 2\sqrt{x} - 3 \cos z = 3 $$$$ 2 x - z^2 = 18 $$