Maximizing Constrained Optimization Problem

In summary, there is a typo in the given problem, which should be corrected to R > n max (1≤i≤n) σi − (Σ n i=1 σi ) in order to proceed with part B. Screenshots are not allowed in PF, so please type out the problem and solution for assistance.
  • #1
hellomrrobot
10
0

Homework Statement


Snip20151102_3.png

There is a typo in the problem, ”R > Σ n i=1 σi − n max 1≤i≤n σi” which should be R > n max (1≤i≤n) σi − (Σ n i=1 σi )

Homework Equations

The Attempt at a Solution


Snip20151102_4.png

Not sure where to go with part B or where to start...
 
Physics news on Phys.org
  • #2
hellomrrobot said:

Homework Statement


View attachment 91270
There is a typo in the problem, ”R > Σ n i=1 σi − n max 1≤i≤n σi” which should be R > n max (1≤i≤n) σi − (Σ n i=1 σi )

Homework Equations

The Attempt at a Solution


View attachment 91271
Not sure where to go with part B or where to start...

If you type out the problem and solution I will be glad to look at it; otherwise, not. (Screenshots are not illegal in PF, but are strongly discouraged, and many helpers will not look at them, and for good reasons. See the pinned article "Guidelines for helpers and students", by Vela).
 

1. What is constrained optimization?

Constrained optimization is a mathematical technique used to find the maximum or minimum value of a function subject to a set of constraints. The constraints limit the possible values that the function can take, making it a more realistic and practical problem to solve.

2. What are the types of constraints in constrained optimization?

There are two main types of constraints in constrained optimization: equality constraints and inequality constraints. Equality constraints require that a function's value must equal a specified value. Inequality constraints require that a function's value must be greater than or less than a specified value.

3. How is constrained optimization different from unconstrained optimization?

Constrained optimization takes into account restrictions or limitations on the values that a function can take, while unconstrained optimization does not have any restrictions on the function's values. This makes constrained optimization a more complex problem to solve.

4. What are the common techniques used in constrained optimization?

Some common techniques used in constrained optimization include the Lagrange multiplier method, the KKT conditions, and the gradient projection method. These methods help to find the optimal solution to a constrained optimization problem.

5. In what fields is constrained optimization commonly used?

Constrained optimization is used in various fields such as economics, engineering, finance, and operations research. It is particularly useful in situations where there are limited resources or when there are certain constraints that must be considered in decision-making processes.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
520
  • Calculus and Beyond Homework Help
Replies
4
Views
798
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
989
  • Calculus and Beyond Homework Help
Replies
2
Views
627
  • Calculus and Beyond Homework Help
Replies
3
Views
467
  • Calculus and Beyond Homework Help
Replies
6
Views
275
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top