Optimization algorithms for risk management in multidimensional Gaussian systems

The paper presents a comparative analysis of optimization algorithms to solve the risk management problem in Gaussian stochastic systems. The optimization task considered in the work has a number of features that need to be taken into account in the solution. The features of the problem are the presence of a stochastic restriction on the required level of risk, the non-convexity of the area of admissible decisions and the increase in the number of control variables in the task of achieving an acceptable level of risk. There are proposed ways of solving the problem of the occurrence of a set of local minimums. The study of the effectiveness of the zero, first and second-order methods for solving the problem of unconditional minimization using the Monte Carlo statistical test method is carried out. Each method was adapted to the specifics of the problem being solved. The software implementation of all presented algorithms was performed. The article presents the results of the study. The computational complexity of algorithms is calculated.