Nonlinear programming algorithms

The subject of the research is nonlinear programming methods used to solve optimization problems in which the objective function, constraints, or both are nonlinear in nature. Unlike linear programming, nonlinear problems have a more complex structure, which increases their versatility, but at the same time complicates the analysis and search for solutions. The paper considers two key algorithms: Sequential quadratic programming (SQP) is a method based on the iterative solution of quadratic subproblems approximating the original nonlinear problem and is especially useful for problems where the objective function and constraints have a nonlinear relationship. The Interior Point Method is an efficient algorithm for problems with constraints, characterized by high convergence rate and versatility. In the course of the research, theoretical methods were used, including: Search and analysis of literature on nonlinear programming methods. Comparative analysis of SQP algorithms and internal points. The output of mathematical equations describing the optimization of chemical and technological processes using nonlinear programming. Special attention is paid to software implementations such as Interior Point OPTimizer, which uses the interior point method. The main conclusions of the study are: Nonlinear programming is a powerful tool for solving complex optimization problems, especially in chemical technology. The choice of method depends on the problem structure, the type of constraints, and the required accuracy: SQP is effective for problems with nonlinear objective functions and constraints, but requires precise definition of active constraints. The interior point method avoids this problem by using barrier functions, which makes it more stable. The main disadvantage of SQP is the need for complete identification of active constraints, whereas the interior point method demonstrates better convergence in complex cases. The novelty of the work lies in the comprehensive analysis and comparison of SQP methods and internal points in relation to the optimization of chemical and technological processes. The key features and limitations of each method are systematized. Their effectiveness is evaluated using the example of problems with nonlinear constraints. The practical aspects of implementing algorithms in modern software packages are considered. The results of the work can be useful for choosing the optimal method of nonlinear optimization in engineering and technological applications.