Abstract
The solution of inverse problems is considered taking into account the restrictions using inverse calculations. An algorithm is proposed for solving the inverse problem, taking into account restrictions while minimizing the sum of the absolute values of the changes in the arguments. The problem of determining the increments of the function arguments is presented as a linear programming problem. The algorithm includes solving the inverse problem with the help of inverse calculations while minimizing the sum of the absolute changes in the arguments, checking the correspondence of the obtained arguments to the given restrictions, adjusting the value of the argument if it goes beyond the limits of acceptable values, and changing the varied arguments to achieve the given value of the resulting indicator. The solution of two problems with the additive and mixed dependence between the arguments of the function is considered. It is shown that the solutions obtained in this case are consistent with the result of using an iterative procedure based on changing the resulting value to a small value until a given result is achieved, and the results are compared with solving problems using the MathCad mathematical package. The advantage of the algorithm is a smaller number of iterations compared to the known method, as well as the absence of the need to use coefficients of relative importance. The presented results can be used in management decision support systems
Highlights
Tasks to be solved in the field of economics can be divided into direct and reverse in the direction of causal relationship
An algorithm is proposed for solving the inverse problem using inverse calculations while minimizing the sum of the absolute changes in the arguments, taking into account restrictions on the values of the arguments
An algorithm is proposed for solving the inverse problem while minimizing the sum of the absolute increments of the arguments, taking into account restrictions on the values of the arguments
Summary
Tasks to be solved in the field of economics can be divided into direct and reverse in the direction of causal relationship. In [15], an algorithm is proposed for solving the problem in the presence of restrictions, including the gradual change of the resulting indicator to a small step value and the determination of the argument values using inverse calculations using the coefficients of the relative priority of the arguments. The presented work is devoted to the development of an algorithm for solving the inverse problem with a minimum total absolute change in the arguments, taking into account the limitations Unlike existing works, this algorithm will not require multiple solutions to the inverse problem with a sequential approximation of the initial value of the resulting indicator to the given one, the maximum number of iterations will be equal to the number of arguments whose values are constrained.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
