An optimization problem is a mathematical problem that involves finding the best solution from all possible options, given a set of constraints. It is often used to maximize or minimize a specific objective function.
A local minimum is a point within the feasible set where the objective function has the lowest value compared to all other neighboring points. However, it is not necessarily the overall lowest value for the entire feasible set.
A feasible set is the set of all possible solutions that satisfy the given constraints in an optimization problem. It is the region within which the optimal solution can be found.
The global minimum is the lowest value of the objective function for the entire feasible set. To determine if you have found the global minimum, you can test different points within the feasible set and compare the objective function values. If the value at a certain point is lower than all other points, it is likely the global minimum. However, in some cases, it may be difficult to determine if the global minimum has been found without testing all possible points.
Yes, a feasible set can have multiple local minima. This means that there are multiple points within the feasible set where the objective function has the lowest value compared to all other neighboring points. However, only one of these local minima can be the global minimum.