A new algorithm for solving a system of linear inequalities using the accelerated Fejér process of searching for a non-negative solution to a system of linear algebraic equations is presented. The Part 1 of this paper presents the theoretical justification of the algorithm and the results of a preliminary (illustrative) computational experiment on a system of medium-dimensional inequalities with real industrial data. The experimental results demonstrate the operability of the proposed algorithm and its higher convergence rate (estimated by the spent time and the number of performed iterations) compared to the three main variants of the “classical” Fejér algorithms for solving systems of linear inequalities based on the strategies of weighted, sequential, and extreme combining of Fejér projection mappings onto half-spaces corresponding to the individual inequalities of the inequality system under study. A more detailed experimental study of the proposed algorithm will be performed in Part 2 of the paper.
Erokhin et al. (Sun,) studied this question.
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