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How is a constrained optimization problem converted to an unconstrained optimization problem?1 pointWith the help of duality theoremWith the help of Lagrangian multiplierWith the help of Gaussian multiplierWith the help of Laplacian

Question

How is a constrained optimization problem converted to an unconstrained optimization problem?1 pointWith the help of duality theoremWith the help of Lagrangian multiplierWith the help of Gaussian multiplierWith the help of Laplacian

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Solution

A constrained optimization problem can be converted to an unconstrained optimization problem with the help of the Lagrangian multiplier. Here are the steps:

  1. Define the objective function: This is the function that you want to maximize or minimize.

  2. Define the constraints: These are the restrictions or limitations on the decision variables.

  3. Form the Lagrangian: The Lagrangian is a function that incorporates the objective function and the constraints. It is formed by subtracting the product of a Lagrange multiplier and the constraint from the objective function.

  4. Solve the Lagrangian: The solution to the Lagrangian gives the values of the decision variables that maximize or minimize the objective function subject to the constraints.

  5. Check the second-order conditions: The second-order conditions are used to determine whether the solution is a maximum, minimum, or saddle point.

So, the correct answer is "With the help of Lagrangian multiplier".

This problem has been solved

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