MA208 Optimisation Theory
Solutions to Exercises 1 (Real numbers)
Solution to Exercise 1.1.
Let A have n elements, A = cfw_ a1 , a2 , . . . , an . We prove the claim by induction on n. If
n = 1, then
MA208 Optimisation Theory
Solutions to Exercises 3 (Algorithms, BellmanFord)
Solution to Exercise 3.1.
When the array elements are S[1], S[2], S[3], S[4], S[5], S[6] = 5, 3, 3, 4, 3, 8, then their
min
MA208 Optimisation Theory
Solutions to Exercises 2 (Digraphs)
Solution to Exercise 2.1.
(a) For a directed graph D = (V, A), the arcs are a set of ordered pairs (u, v) with
u, v V, u = v. Because A is
MA208 Optimisation Theory
Exercises 6 (Functions on R2)
Exercise 5.1.
Consider the function f : R2 R, mentioned in the lecture, defined by
0
if ( x, y) = (0, 0)
xy
f ( x, y) =
otherwise.
2
x + y2
(a)
2014 examination Solutions
Answers MA208, Optimisation Theory
Each question gives 25 marks.
1
(a) ( 8 marks )
The Weierstrass Theorem cannot be applied directly because the domain [0, ) of the functio
2015 examination Solutions
Answers MA208, Optimisation Theory
Each question gives 25 marks.
1
Skills tested: Understanding of basic concepts about closed and open sets and applying them in
new context
Summer 2013 examination
MA208
Optimisation Theory
Half Unit
1 Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many ques
Summer 2014 examination
MA208
Optimisation Theory
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This examination paper contains 5 questions. You may attempt
Solutions for the MA208 Exam (Summer 2013)
1
(a) (i) (Essentially bookwork; ) The rst version of the Bellman-Ford algorithm computes exactly these d(v; i). The algorithm (without checking for a negati
Summer 2015 examination
MA208
Optimisation Theory
(Half Unit)
2014/2015 syllabus only not for resit candidates
Instructions to candidates
Time allowed: 2 hours
This examination paper contains 5 questi