cateater2000 said:The minimizer is the point t where the minimum is. THat's why I'm a bit confused with the question. The wording I was given in my book is a bit awkward.
I think what it means is. For every f(x1,x2) given that x1 and x2 are lines.
There is a minimum at t=0
Those that make sense?
A strict local minimizer is a point in a multivariate function where the function reaches its lowest value within a specific neighborhood. This means that there is no other point nearby that has a lower value than the strict local minimizer.
A local minimizer is a point where the function reaches a low value, but it may not be the lowest value in its neighborhood. A strict local minimizer, on the other hand, is the lowest value in its neighborhood and there is no other point nearby with a lower value.
A strict local minimizer can be calculated using various optimization algorithms such as gradient descent, Newton's method, or the BFGS method. These algorithms use the gradient or Hessian matrix of the function to find the point where the gradient is equal to zero, indicating a minimum.
The concept of strict local minimizer is important in optimization because it helps to identify the most optimal point in a multivariate function. By finding the strict local minimizer, we can determine the best solution or set of parameters that minimizes the function and achieve the desired results.
Yes, a function can have multiple strict local minimizers. This is especially common in complex and highly dimensional functions. In such cases, it is important to carefully analyze the function and choose the most appropriate optimization algorithm to find the global minimum, which is the absolute lowest value of the function.