Statistical estimation of accuracy in conditionally extremal problems

The paper is concerned with a statistical method for estimating the optimal value of the objective functional in conditionally extremal problems. The method uses extreme distributions of random quantities for description of sequences of values of the objective functional generated in operation of suboptimal algorithms. It is shown that in solution of medium and high dimension problems the behaviour of regular algo­ rithms is near-statistical and the use of the statistical approach to estimation of algo­ rithm accuracy estimation becomes justified. Applications of the method to problems of integer linear, nonlinear, and stochastic programming are considered and results of computing experiments given.