Final answer:
The order of optimization problems from fastest to slowest is: Linear programming, Quadratic programming, Nonlinear programming, Mixed integer programming.
Step-by-step explanation:
The order of optimization problems from fastest to slowest is:
- Linear programming
- Quadratic programming
- Nonlinear programming
- Mixed integer programming
Linear programming involves optimizing a linear objective function along with linear equality and inequality constraints. It can be solved efficiently using algorithms such as the simplex method.
Quadratic programming deals with optimizing a quadratic objective function subject to linear constraints. It is generally slower than linear programming but faster than nonlinear programming.
Nonlinear programming includes optimization problems with nonlinear objective functions and constraints. These problems are more complex to solve and typically require iterative methods.
Mixed integer programming adds the additional requirement that some decision variables must take integer values. This introduces additional complexity and makes solving these problems slower than other types of optimization problems.