What are the key concepts of Lagrange Multipliers?

Click For Summary
SUMMARY

The discussion centers on the key concepts of Lagrange Multipliers, a technique used in multidimensional calculus to find local maxima and minima of functions subject to constraints. Participants seek clarity on the role of constraints, the interpretation of the additional variable in the method, and alternative approaches to achieve similar results. The conversation highlights the need for visual understanding of the function's graph rather than its applications in fields like economics. The importance of partial differentiation in this context is also emphasized, particularly regarding the differentiation of planes.

PREREQUISITES
  • Understanding of multidimensional calculus
  • Familiarity with partial differentiation
  • Basic knowledge of optimization techniques
  • Graphical interpretation of functions
NEXT STEPS
  • Study the graphical representation of functions in multidimensional calculus
  • Learn about alternative optimization methods, such as the method of steepest descent
  • Explore the implications of constraints in optimization problems
  • Review case studies where Lagrange Multipliers are applied in real-world scenarios
USEFUL FOR

Students of calculus, mathematicians, and anyone interested in optimization techniques in multidimensional spaces will benefit from this discussion.

mtanti
Messages
172
Reaction score
0
I've just started multi dimensional calculus, among which Langrange's Multipliers. I have some questions which will help me grasp the concepts since I'm a very curious guy...

a) What are you finding exactly with this technique?
b) What is the constraint?
c) What does the extra variable represent?
d) Is there another more intuitive but less effiecient way to obtain the same result?

My lecturer is a very poor teacher and just wants to get on with the syllabus I guess... I would like an explanation on the actual graph of the function and not about the practical usage of it such as in economics...

P.S. I understood the reasoning behind partial differentiation but I'm still shakey on the fact that to differentiate a plane you can only find a general gradient for each axis (y and x) and not a single general gradient function f'(x,y).

Thanks!
 
Physics news on Phys.org
Already been there... I was looking for something different...
 

Similar threads

Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
MHB Holly's questions at Yahoo Answers regarding Lagrange multipliers
  • · Replies 1 ·
Replies
1
Views
3K
High School Constrained Optimization with the KKT Approach
  • · Replies 7 ·
Replies
7
Views
2K
Can't get Lagrange multiplier to work in a single exercise
  • · Replies 16 ·
Replies
16
Views
3K
Lagrange Multipliers in Calculus of Variations
  • · Replies 4 ·
Replies
4
Views
4K
Constrained Optimization via Lagrange Multipliers
  • · Replies 10 ·
Replies
10
Views
6K
Solve Highest/Lowest Points on Curve of Intersection with Lagrange Multipliers
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Lagrange multipliers and critical points
  • · Replies 7 ·
Replies
7
Views
2K
MHB Finding Extrema with Lagrange Multipliers
  • · Replies 9 ·
Replies
9
Views
2K
MHB What are the steps for solving a problem using Lagrange Multipliers?
  • · Replies 9 ·
Replies
9
Views
2K