Justification and development of an adaptive algorithm for stochastic optimization of a multi-criteria process

Abstract

The paper considers aspects of the development of algorithms for optimizing complex systems, and also develops an algorithm for solving problems of convex stochastic programming with a non-smooth goal function. The principles of constructing adaptive procedures for adjusting the parameters of variable gradient optimization algorithms are proposed. Note that in almost any iterative algorithm, as a rule, there are parameters that require their adjustment. To control and adjust parameters, - criteria are formed that determine the quality of adjustments. At the same time, the problem of determining the best value of the adjustment parameters belongs to the same class as the original optimization problem. Usually, iterative algorithms that work in the same class of optimization problems are used to adjust the available parameters. Thus, it turns out that two algorithms work simultaneously, in the source space and in the parameter space. Since algorithms are adapted by parameters during operation, this type of algorithm is called adaptive. The current stage of development of computer technology and mathematical support requires the development of algorithms that must function successfully without the User’s participation, both in the process of solving the problem and in the process of finding a solution to the problem. The paper provides recommendations for software implementation of adaptive stochastic algorithms and construction of computational procedures for stochastic computational experiments based on them.