Lecture notes
MATH6184-exercise-1.pdf
- Module
- Machine learning
- Institution
- Abacus College, Oxford
Lecture notes of 2 pages for the course machine learning at Abacus College, Oxford (MATH)
[Show more]
Seller
Follow
Content preview
Prof Dr Jörg Fliege Semester 2, 2022/2023School of Mathematical Sciences
University of Southampton
MATH6184 - Optimization Part
Exercise Sheet 1
You are not required to hand in the answers to these problems.
1. Consider the problem
min 2(x − 3)2
subject to 0 ≤ x ≤ 6.
(a) Verify that this problem is a convex problem.
(b) Verify that the unique solution occurs at x = 3.
(c) Verify that x = 0 and x = 6 are alternate optima if the objective is maximised
instead of minimized.
2. Determine wether each of these nonlinear programming problems is a convex program:
(a)
max ln x1 + 3x2 − x32
subject to x1 ≥ 0,
2x1 + 3x2 − x3 = 1,
x21 + x22 ≤ 9.
(b)
max x1 + x2
subject to x1 x2 ≤ 9,
−5 ≤ x1 ≤ 5,
−5 ≤ x2 ≤ 5.
(c)
max x1 + 6/x1 + 5x22
subject to 4x1 + 6x2 ≤ 35,
x1 ≥ 5,
x2 ≥ 0.
3. A lidless, rectangular box is to be manufactured from cardboard. The cardboard is 30cm
wide and 40cm long.The box is manufactured by cutting away squares from the four
corners of the cardboard, folding up ends and sides, and joining them with heavy type.
The designer wishes to choose box dimensions that maximise the volume of the box.
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller 1097434525U. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £3.16. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
85443 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now