Math 309 HW2 - Adam Oberman Math

Sec 2.2 Feasibility and Optimality

When the problem says graph, this means sketch, using calculus, not plot using mathematical software.

• Warm up: 2.1, 2.2, 2.3, 2.4 (typical quiz/exam questions)
• Counterexample/Definitions: 2.5 2.6

Sec 2.3 Convexity

• Proofs using definitions: 3.1, 3.2, 3.3, 3.4, and: 3.0 (below) (typical proof quiz/exam question: 3.0, 3.1, 3.3, 3.5, 3.6)
  • 3.0 Prove using the definition of convex function, that the maximum of two convex functions is convex.
• More challenging: 3.9, 3.12, 3.13 (typical harder quiz/exam questions these and 3.16)
• Calculations: 3.18, 3.19, 3.20 (typical calculation questions)

Sec 2.4 General Optimization Algorithm

• 4.1

Sec 2.5 Rates of Convergence

• 5.1,
• 5.0, for the sequences in problem 5.1, plot several terms of the sequence using matlab. Choose a plot which illustrates the convergence. For example get started with the code below. What does the slope of the line tell you?

Example code

k = 1:20;
xk = (1/2).^k;
xk2 = 5*(.1).^(2*k);
semilogy(k,xk, k, xk2)