# ECE580 Homework Assignments

## Spring 2016

• Assignment 1:     Assigned January 15, 2016.     Due by 7:30pm January 22, 2016.
• Problems 1.5, 3.3, 3.8 from the textbook.
• Prove that that if $\Theta$ and $\Sigma$ are convex sets and $\alpha$ and $\beta$ are real numbers, $\alpha\Theta+\beta\Sigma$ is convex. (Pay attention to the details of the proof. See the examples in the text.)
• With the same definitions, prove that the set $\alpha\Theta\cap\beta\Sigma$ is convex. (Be sure to consider all possible cases.)

• Assignment 2:     Assigned January 24, 2016.    Due by 7:30pm January 30, 2016.
• Problems 5.3, 5.4, 5.5, 5.6, 5.9 (use Matlab), and 5.10 from the textbook.

• Assignment 3:     Assigned February 2, 2016.    Due by 7:30pm February 8, 2016.
• Problems 6.1, 6.2, 6.9, 6.13, and 6.14 from the textbook.

• Assignment 4:     Assigned February 8, 2016.    Due by 7:30pm February 15, 2016.
• Problems 7.10, 9.3, 9.4, 8.1, and 8.8 from the textbook.

• Assignment 5:     Assigned February 15, 2016.    Due by 7:30pm March 2, 2016.
• Problems 10.10, 10.11, 11.1, and 11.7 from the textbook.

• Assignment 6:     Assigned March 9, 2016.    Due by 7:30pm March 23, 2016.
• Problems 12.3, 12.8, 12.14, 12.19, and 12.32 from the textbook.

• Assignment 7:     Assigned March 23, 2016.    Due by 7:30pm March 30, 2016.
• Problems 13.1, 13.5 from the textbook, plus the following problems: write scripts in Matlab to apply the Nelder-Mead algorithm and the PSO algorithm to find the minimizer of $f(x) = x_1 e^{-x_1^2 - x_2^2}$.
• Assignment 8:     Assigned April 13, 2016.    Due by 7:30pm April 25, 2016.
• Problems 2.6.1, 2.6.3, 2.6.4, 3.11.8, and 3.11.9 from Luenberger and Ye.
• (Highly Recommended) Optional Assignment 9:     Assigned April 25, 2016.    Due by 7:30pm May 2, 2016.
• Problems 20.1, 20.2(b), 20.7, 20.9, 20.15, and 21.1
• (Highly Recommended) Optional Assignment 10:     Assigned April 25, 2016.    Due by 7:30pm May 2, 2016.
• Problems 21.2(c), 21.5, 21.6, 21.7, 21.8, 21.17, 21.18, 21.19, and 21.20. Turn in at least six of the above problems. Extra points will be awarded for doing more than six. Note the figures in Chapter 22 that show the geometry of problems 21.18 - 21.20. Before solving these problem, use the figure to help you determine the solutions so that you know what the answers should be before you start.