Linearity and nonlinearity are common. Let me talk about something else.
Dynamic programming is an important branch of operational research and an effective quantitative method to solve multi-stage decision-making problems. It was founded by American scholar R. Berman and others. In 2008+095 1, Bellman first proposed to use the optimization principle to solve the multi-stage decision-making problem in dynamic programming, and gave many solutions to practical problems. 59660.8886888866 1
For more than 50 years, dynamic planning has been widely used in engineering technology, enterprise management, industrial and agricultural production, military and other departments, and has achieved remarkable results. In management, dynamic planning can be used for resource allocation, shortest path, inventory, knapsack, equipment update, optimal control and so on. Therefore, dynamic planning is an indispensable tool for scientific decision-making in modern management.
The advantage of dynamic programming is to transform a multi-dimensional decision-making problem into several one-dimensional optimization problems and solve them one by one. This method can't be done by many extreme methods, and it is almost superior to all existing optimization methods. In addition, dynamic programming can find the global maximum or minimum, which is also superior to other optimization methods. It should be pointed out that dynamic programming is a method to solve optimization problems, and it is a way to solve problems, not a new algorithm. Earlier, we learned to solve linear programming problems by simplex method. All mathematical models with linear programming problems can be solved by simplex method, but there is no unified solution method for dynamic programming problems (similar to simplex method). Therefore, when dynamic programming is used to solve optimization problems, it is necessary to analyze specific problems. Aiming at different problems, the corresponding mathematical model is established by using the optimization principle and method of dynamic programming, and then it is solved by dynamic programming method. According to these characteristics of dynamic planning, we should have rich imagination while learning the basic principles and methods of dynamic planning well. Only in this way can the model be established and the optimal solution of the problem be found.
According to whether the time variable is discrete or continuous, the model of dynamic programming problem can be divided into discrete decision-making process and continuous decision-making process, and according to whether the evolution of decision-making process is deterministic or stochastic, the model of dynamic programming problem can be divided into deterministic decision-making process and stochastic decision-making process, namely discrete certainty, discrete randomness, continuous certainty and continuous randomness. We mainly study discrete deterministic models.
2. Stochastic programming and fuzzy programming are two mathematical programming tools to deal with stochastic and fuzzy optimization problems, which are called uncertain programming. The main purpose is to lay the foundation for the optimization theory in uncertain environment. Uncertain programming theory includes three categories: expected value model, machine satisfaction constraint programming and related opportunity programming.
3. The concept of stochastic programming is rare.
You can refer to the branch of operational research.
The research object of mathematical planning is the arrangement and evaluation in planning management. The main problem to be solved is to find the optimal scheme of arrangement according to a certain measurement index under given conditions. It can be expressed as the problem of finding the minimum value of a function under constraints.
Mathematical programming is essentially different from the classical problem of seeking extreme value. Classical methods can only deal with simple expressions and simple constraints. However, in modern mathematical programming, the objective function and constraints of the problem are very complex, and some accurate numerical solutions are needed, so the research on the algorithm is particularly valued.
The simplest problem here is linear programming. If the constraint and objective function are linear, it is called linear programming. To solve linear programming problems, linear equations should be solved theoretically, so the method of solving linear equations and the knowledge of determinant and matrix are very necessary tools in linear programming.
The emergence of linear programming and its solution-simplex method has greatly promoted the development of operational research. Many practical problems can be solved by linear programming, and simplex method is an effective algorithm, and the emergence of computers makes the solution of some large and complex practical problems become a reality.
Nonlinear programming is the further development and continuation of linear programming. Many practical problems, such as design problems and economic balance problems, belong to the category of nonlinear programming. Nonlinear programming not only expands the application scope of mathematical programming, but also raises many basic theoretical problems for mathematicians, which makes convex analysis and numerical analysis in mathematics develop. There is also a time-related planning problem called "dynamic planning". In recent years, it has become an important tool commonly used in optimal control problems in engineering control, technical physics and communication.
Queuing theory is another branch of operational research, which is called stochastic service system theory. The purpose of its research is to answer the question of how to improve the service objects of service institutions or organizations and make some indicators reach the optimal level. For example, how many docks should a port have and how many maintenance personnel should a factory have.
Queuing theory was first studied by Danish engineer Erlang in the early 20th century on the efficiency of telephone exchange. In order to estimate the capacity of airport runway in World War II, it has been further developed, and its corresponding discipline renewal theory and reliability theory have also been developed.
Because queuing phenomenon is a random phenomenon, probability theory is mainly used as the main tool to study queuing phenomenon. In addition, there are differential and differential equations. Queuing theory describes the image of the object it wants to study when customers come to the service desk to ask for reception. If the service desk is occupied by other customers, there will be a queue. On the other hand, the service desk is sometimes idle and sometimes busy. It is necessary to obtain the probability distribution of customer waiting time and queue length by mathematical method.
Queuing theory is widely used in daily life, such as the regulation of reservoir water volume, the arrangement of production line, the dispatching of railway approach, the design of power grid and so on.
Game theory is also called game theory. The aforementioned horse racing in Tian Ji is a typical game theory problem. As a branch of operational research, the development of game theory is only a few decades. The mathematician who systematically founded this subject is now recognized as the Hungarian-American mathematician and the father of computers-von Neumann.
At first, the study of game theory by mathematical methods began with chess-how to determine the winning method. Because this is a problem of studying the conflict between the two sides and winning countermeasures, this subject has very important applications in the military. In recent years, mathematicians have also studied the fighting and tracking between mines and ships, fighters and bombers, and put forward a mathematical theory that both sides can make decisions independently. In recent years, with the further development of artificial intelligence research, more new requirements have been put forward for game theory.
Search theory is a branch of operational research that emerged because of the need of war in the Second World War. This paper mainly studies the theory and method of how to design and find the optimal scheme of a certain target and implement it under the condition of limited resources and detection means. In World War II, the allied air force and navy were born in the process of studying how to identify the submarine activities, fleet transportation and force deployment of the Axis countries. Search theory has also made many achievements in practical application. For example, in the 1960s, the United States successfully searched for the nuclear submarines "oil tankers" and "scorpions" missing in the Atlantic Ocean and the hydrogen bombs missing in the Mediterranean Sea.
The application field of operational research is very wide, which has penetrated into service, inventory, search, population, confrontation, control, timetable, resource allocation, site selection, energy, design, production, reliability and so on.
Queuing theory and stochastic programming should be close.
Specifically, I hope you can consult a professional teacher.
I hope it helps you.