A Method for Problem Solving Dynamic Programming Using Quadratic Inequalities and Convex Monotonicity Theory

Dynamic programming is an important discipline in the fields of applied mathematics, operations, and computer science, and standard solution methods are used in various fields of engineering, economics, commerce, management, etc. Dynamic programming is that, whatever the initial state of optimality and the initial control, a sequence of subsequent controls with respect to the resulting state must be the optimal strategy. Thus, it is an optimization method that solves problems in a time-dependent process using the principle of optimality for economic problems that cannot be solved by linear programming. The continued emergence of publications describing new settings, reformulations and general theory in the development of dynamic programming demonstrates the continuing interest in the fundamental problems of dynamic programming. In this paper, we introduce an acceleration method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. And we prove that the acceleration method using decision monotonicity is effective in improving the execution time when the input data is large compared to the existing method. We also consider the execution time when the mathematical model of the plant is referred to as dynamic programming and the state transition equation satisfies convex monotonicity. We have used the quadrilateral inequality and convex monotonicity theory to solve the traditional computational complexity and time-increasing problem and find reasonable solutions quickly and accurately. In this paper, we introduce an accelerated method to improve the execution time, which is the most challenging problem in solving many real-life dynamic programming problems. We define the quadrilateral inequality and convex monotonicity theory and consider the acceleration of the dynamic programming solution of the mathematical model satisfying it.