First, linear programming
Linear programming is one of the most basic and common types in mathematical programming. Its goal is to find the variable value that makes a linear objective function reach the maximum (or minimum) value under a set of linear constraints. The decision variables and constraints of linear programming model are linear, so it can be solved by linear algebra.
Second, integer programming.
Integer programming is an extension of linear programming, which requires decision variables to take integer values. Integer programming has important practical value in practical applications such as production scheduling and resource allocation. However, due to the complexity of integer programming problem, its solving process is more difficult, and special algorithms and skills are needed to solve it, such as branch and bound method and cutting plane method.
Third, nonlinear programming.
Nonlinear programming is a programming problem that introduces variables in objective functions or constraints into nonlinear relationships. In nonlinear programming, the objective function and constraints can be polynomials, exponential functions or other nonlinear functions. Because of the complexity of nonlinear programming problems, iterative method is generally needed to approximate the optimal solution.
Fourth, dynamic planning.
Dynamic programming is a method to solve the whole problem step by step by decomposing a complex problem into simple subproblems and using the relationship between the subproblems. It is usually used for problems with overlapping subproblems and optimal substructure characteristics. Dynamic programming considers the possible future situation in the decision-making process and solves it by establishing recursive relations.
Verb (abbreviation of verb) random programming
Stochastic programming is a programming problem that introduces random variables into decision variables and constraints. It considers uncertain factors in the decision-making process and solves them through probability model and stochastic programming technology. Faced with high risk and uncertainty, stochastic programming has important application value, such as financial risk management and supply chain optimization.
Six, multi-objective planning
Multi-objective programming is a programming problem that considers multiple independent objective functions in a decision-making problem. The goal of multi-objective programming is to find a set of solutions so that all objective functions can achieve the best possible results. The commonly used methods of multi-objective programming include weighting method, constraint method and Pareto optimal solution.
Mathematical programming is a subject that studies how to solve the optimization problem under constraints through mathematical methods and skills. It covers different models and methods such as linear programming, integer programming, nonlinear programming, dynamic programming, stochastic programming and multi-objective programming.
Mathematical programming has extensive application value in practical application, which can help people make more reasonable and better decisions in various fields.