Adaptive thresholding technique for solving optimization problems on attainable sets of (max, min)-linear systems

summary:This article develops a parametric method depend on threshold technique for solving some optimization problems on attainable sets of so called (max, min)-separable linear systems. The concept of attainable set for (max, min)-separable linear equation systems will be introduced. Properties of the attainable sets will be studied in detail. The (max, min) - separable linear equation systems, in which the function of unknown variable occur only on one side, will be consider. The main idea of the proposed algorithm is that we will begin the calculations with the maximum element and we will try to decrease the value of the objective function of our problem, by decreasing its components in such a way that they stay within attainable set. Optimization problem consisting in finding the nearest point of an attainable set to a given fixed point will be considered. An algorithm for solving the optimization problem will be proposed. Motivational example from the area of operations research, which shows possible applications of the optimization problem solved in this paper, will be given. Numerical example illustrating the proposed algorithm is included