What does WSOC mean in UNCLASSIFIED
WSOC stands for Weak Second Order Condition. It is an economic concept used in optimization problems to ensure that the solution found is a local minimum.
WSOC meaning in Unclassified in Miscellaneous
WSOC mostly used in an acronym Unclassified in Category Miscellaneous that means Weak Second Order Condition
Shorthand: WSOC,
Full Form: Weak Second Order Condition
For more information of "Weak Second Order Condition", see the section below.
Meaning of WSOC
In optimization, the second derivative of a function at a given point determines whether the point is a local minimum, maximum, or saddle point. A WSOC states that the second derivative of a function at a local minimum must be positive definite. This means that the function must be strictly convex in the neighborhood of the local minimum.
Significance of WSOC
WSOC is important because it ensures that the solution found is a local minimum, not a saddle point. A saddle point is a point where the first derivative is zero, but the second derivative is not positive definite. This means that the function can both increase and decrease in different directions from the saddle point, making it difficult to determine the true minimum.
Essential Questions and Answers on Weak Second Order Condition in "MISCELLANEOUS»UNFILED"
What is the Weak Second Order Condition (WSOC)?
In optimization, the Weak Second Order Condition (WSOC) is a sufficient condition for a local minimum to be a global minimum. It states that the Hessian matrix, which is the matrix of second partial derivatives of the objective function, must be positive semi-definite at the local minimum. This means that the objective function must be concave in the neighborhood of the local minimum.
When is the WSOC satisfied?
The WSOC is satisfied when the Hessian matrix is positive definite, which means that all of its eigenvalues are positive. This implies that the objective function is strictly concave in the neighborhood of the local minimum.
Why is the WSOC important?
The WSOC is important because it provides a guarantee that a local minimum is also a global minimum. This is useful in practice because it allows us to find global minima efficiently using local optimization algorithms.
What are some limitations of the WSOC?
The WSOC is not necessary for a local minimum to be a global minimum. It is only a sufficient condition. Additionally, the WSOC can be difficult to verify in practice, especially for high-dimensional problems.
Final Words: WSOC is a mathematical condition used in optimization problems to ensure that the solution found is a local minimum. By ensuring that the second derivative is positive definite, WSOC helps to eliminate saddle points and identify the true minimum of the function.
WSOC also stands for: |
|
| All stands for WSOC |