How to find global/local minimums/maximums.

  • Context: Undergrad 
  • Thread starter Thread starter thomasxc
  • Start date Start date
Click For Summary
SUMMARY

This discussion focuses on methods to find global and local minimums and maximums in various mathematical contexts. Key techniques include using derivatives for functions of one variable, applying gradients and Lagrange multipliers in multivariable calculus, and utilizing calculus of variations for functionals. Additionally, linear programming is essential for linear functionals defined on convex sets, while integer programming is applicable for functions of integer variables. These methods are foundational in optimization across different mathematical disciplines.

PREREQUISITES
  • Understanding of derivatives in single-variable calculus
  • Familiarity with gradients and Lagrange multipliers in multivariable calculus
  • Knowledge of calculus of variations for functionals
  • Basic principles of linear and integer programming
NEXT STEPS
  • Study the application of derivatives in single-variable optimization
  • Learn about gradients and Lagrange multipliers in multivariable calculus
  • Explore the calculus of variations and its applications
  • Investigate linear programming techniques for optimization problems
USEFUL FOR

Mathematicians, engineering students, and anyone interested in optimization techniques across various mathematical fields.

thomasxc
Messages
140
Reaction score
0
i've been searching the entire internet looking for a good how-to, but i have had no success. this is not a homework question, i am simply interested. and i would greatly appreciate some straightforward instruction.thanks in advance.
 
Physics news on Phys.org
For function of one variable ... a course on calculus: this is one of the standard applications of derivatives.

For function of n real variables ... a course on multivariable calculus. Gradients, Lagrange multipliers, etc.

For a functional depending on a function ... "calculus of variations"

For linear functional defined on a convex set ... "linear programming"

For function of integer variables ... "integer programming"
 
See this http://en.wikipedia.org/wiki/Maxima_and_minima" .
 
Last edited by a moderator:

Similar threads

Undergrad What Exactly is Step Size in Gradient Descent Method?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Oddity of a functional equation for the R zeta function
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Gradient descent algorithm and optimizers
  • · Replies 5 ·
Replies
5
Views
2K
MHB Finding roots of this particular polynomial
  • · Replies 4 ·
Replies
4
Views
2K
MHB Find the global extrema of this function over the given region
  • · Replies 10 ·
Replies
10
Views
3K
MHB Finding maximum/minimum values?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Proving Global Max/Min for Function w/ 2 Variables: Advice Needed
  • · Replies 5 ·
Replies
5
Views
4K
MHB Find the coordinates and the nature of any turning points (maximum and minimum)
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Principle of minimum action and application to real problems
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Why do functions have maximum and minimum values in intervals?
  • · Replies 6 ·
Replies
6
Views
3K