CONCORDIA UNIVERSITY
FACULTY OF ENGINEERING AND COMPUTER SCIENCE

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ENCS6181 Optimization Techniques (4 credits)

Date issued: November 1, 2019 Prof. Luis Rodrigues Date due: November 29, 2019
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Please do this work on your own and come talk to me about any questions you may have.
In your final report you must include the following:
1. A statement of any assumptions you have made and why you have made them
2. Matlab plots showing the result of your algorithm
3. Your Matlab .m files commented with headers indicating how each function is used
4. Please keep the written part of your report to within 10 pages. You can include as
many figures and code you want in an appendix. The report should be formatted
using the standard IEEE format for research papers.
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Project Description

Please choose one of the following two options:

1) Propose your own project. Pick an application in your field of interest that can be
formulated as an optimization problem. You must email me your proposal by November
5, before 5pm.

2) Solve the problem described next.


Proposed Problem

Your job is to program an algorithm in Matlab using sequential unconstrained optimization to
find the maximum volume rectangle R that it contained in a polytope P. The rectangle and the
polytope are defined as follows:
= ∈ !  |   ≤ ≤ , where l, u are lower and upper bound vectors, respectively = ∈ !  |   ≤ , where A,b have appropriate dimensions and > 0

Hint: Show first that the constraint of the rectangle being contained in the polytope can be
described by ! − ! ≤ where !"! = max 0,!" ,!"! = max 0,−!" and use as an
optimization functional − ! − !! . The matlab function syntax should be
[l,u]=maxvolrectangle(A,b).

The function must plot the polytope and the maximum volume rectangle enclosed by the
polytope. Your code must compute a rectangle within 1% of the optimal volume. I will try all
codes in the same example (i.e, for the same A and b).