1, definition and category: Mathematical programming model is a form of mathematical modeling, which is usually used to describe and solve various practical problems including optimization problems. It is a process of transforming practical problems into mathematical forms. Optimization model is a specific subset of mathematical programming model, and its focus is to find the optimal solution, that is, to maximize or minimize the objective function value under given constraints.
2. Objective: Mathematical programming models can be used to solve different types of problems, including but not limited to optimization problems. It can be used in many problems, such as constraint satisfaction, decision analysis, task allocation and so on. The optimization model focuses on solving the optimization problem, and seeks the optimal solution by maximizing or minimizing the objective function, such as cost minimization, profit maximization, optimal path, etc.
3. Constraints: Both mathematical programming model and optimization model involve the handling of constraints. Mathematical programming model can contain many kinds of constraints, such as linear constraints, nonlinear constraints, equality constraints, inequality constraints and so on. The optimization model needs to find the optimal solution under the given constraints. Although there are differences between mathematical programming model and optimization model, they often cross and merge with each other in practical application. Optimization problem is usually regarded as an important subset of mathematical programming problem, and mathematical programming methods and techniques are widely used in the process of modeling and solving optimization problems. Therefore, it can be said that the optimization model is a concrete form of mathematical programming model, which is used to solve the optimization problem.