Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Matlab Optimization Toolbox: Constrained Optimization Example, Schemes and Mind Maps of Law of Torts

Ecole National d'Agriculture de MeknesLaw of Torts

A tutorial on using the matlab optimization toolbox to solve a constrained optimization problem. It includes step-by-step instructions for writing the objective function and non-linear constraints, running the optimization with different starting points, and analyzing the results. The goal is to maximize the given objective function subject to various inequality constraints on the variables x1 and x2. This document would be useful for students studying numerical optimization, mathematical programming, or matlab programming in the context of engineering, applied mathematics, or computer science courses. It could serve as study notes, lecture notes, or an assignment for university-level courses related to optimization, matlab, or numerical methods.

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 12/20/2022

osama-emsi
osama-emsi ๐Ÿ‡ฒ๐Ÿ‡ฆ

5 documents

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Preliminary work with Matlab programming
Read carefully the tutorial on Matlab Optimization Toolbox and program the Constrained Optimization
Example: Inequalities (https://fr.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html).
Questions:
Solve the optimization problem below:
๐‘š๐‘Ž๐‘ฅ (๐‘ฅ1+ ๐‘ฅ2โˆ’10)2
30 +(๐‘ฅ1โˆ’ ๐‘ฅ2+10)2
120
๐‘ . ๐‘ก.
๐‘ฅ1
2. ๐‘ฅ2โ‰ฅ 5
(๐‘ฅ1+ ๐‘ฅ2โˆ’ 5)2
30 +(๐‘ฅ1โˆ’ ๐‘ฅ2โˆ’12)2
120 โ‰ฅ 1
๐‘ฅ1
2+ 8๐‘ฅ2โ‰ค75
๐‘ค๐‘–๐‘กโ„Ž 0 โ‰ค ๐‘ฅ1โ‰ค10
0 โ‰ค ๐‘ฅ2โ‰ค10
a) Write the Matlab functions for the objective function and non-linear constraints and
upload them.
b) Write the Matlab script to run optimization and upload it.
c) Set the starting point at the center of the search space (๐‘ฅ1= 5, ๐‘ฅ2= 5) and run
optimization. Is the optimization successful? What are the best values of objective and
variables?
d) Set the starting point at (๐‘ฅ1= 0, ๐‘ฅ2= 0) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
e) Set the starting point at (๐‘ฅ1=10, ๐‘ฅ2=10) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
f) Set the starting point at (๐‘ฅ1= 0, ๐‘ฅ2=10) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
g) Set the starting point at (๐‘ฅ1=10, ๐‘ฅ2= 0) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
h) Set the starting point at (๐‘ฅ1= 5, ๐‘ฅ2= 0) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
i) Set the starting point at (๐‘ฅ1= 5, ๐‘ฅ2=10) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
j) Set the starting point at (๐‘ฅ1= 0, ๐‘ฅ2= 5) and run optimization. Is the optimization
successful? What are the best values of objective and variables?
k) Set the starting point at (๐‘ฅ1=10, ๐‘ฅ2= 5) and run optimization. Is the optimization
successful? What are the best values of objective and variables?

Partial preview of the text

Download Matlab Optimization Toolbox: Constrained Optimization Example and more Schemes and Mind Maps Law of Torts in PDF only on Docsity!

Preliminary work with Matlab programming

Read carefully the tutorial on Matlab Optimization Toolbox and program the Constrained Optimization Example: Inequalities (https://fr.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html). Questions: Solve the optimization problem below: ๐‘š๐‘Ž๐‘ฅ

(๐‘ฅ 1 + ๐‘ฅ 2 โˆ’ 10 )^2

(๐‘ฅ 1 โˆ’ ๐‘ฅ 2 + 10 )^2

(๐‘ฅ 1 + ๐‘ฅ 2 โˆ’ 5 )^2

(๐‘ฅ 1 โˆ’ ๐‘ฅ 2 โˆ’ 12 )^2

a) Write the Matlab functions for the objective function and non-linear constraints and upload them. b) Write the Matlab script to run optimization and upload it. c) Set the starting point at the center of the search space (๐‘ฅ 1 = 5 , ๐‘ฅ 2 = 5 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? d) Set the starting point at (๐‘ฅ 1 = 0 , ๐‘ฅ 2 = 0 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? e) Set the starting point at (๐‘ฅ 1 = 10 , ๐‘ฅ 2 = 10 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? f) Set the starting point at (๐‘ฅ 1 = 0 , ๐‘ฅ 2 = 10 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? g) Set the starting point at (๐‘ฅ 1 = 10 , ๐‘ฅ 2 = 0 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? h) Set the starting point at (๐‘ฅ 1 = 5 , ๐‘ฅ 2 = 0 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? i) Set the starting point at (๐‘ฅ 1 = 5 , ๐‘ฅ 2 = 10 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? j) Set the starting point at (๐‘ฅ 1 = 0 , ๐‘ฅ 2 = 5 ) and run optimization. Is the optimization successful? What are the best values of objective and variables? k) Set the starting point at (๐‘ฅ 1 = 10 , ๐‘ฅ 2 = 5 ) and run optimization. Is the optimization successful? What are the best values of objective and variables?