Recursive Approach to Solve Linear Optimization Problems

A new approach to solving optimization problems in the field of machine learning is considered. The greatest complexity among such problems is the problem of gradient search for the optimum on the simplex, since in the process of finding a solution it is necessary to implement switching between several expressions of the objective function. The authors propose an approach based on the representation of relations in the form of numerical schemes of backward recursion. The resulting expressions allow you to build more compact computational schemes can implemented in the framework of solving machine-learning problems. The new approach to solving optimization problems in the field of machine learning considered. The greatest complexity among such a problems is the problem of gradient search for the optimum on the simplex, since in the process of finding a solution it is necessary to implement switching between several expressions of the objective function. The authors propose an approach based on the representation of relations in the form of numerical schemes of backward recursion. The resulting expressions give compact computational schemes solving machine-learning problems. When considering range of machine learning tasks, it noted that tuning the model of algorithms according to the initial data is an optimization problem. The practical applicability of machine learning methods largely depends on effectiveness of solving one. The tasks complexity generated by big data leads to the fact that many classical optimization algorithms become inapplicable, because here it is required to solve the problem of optimizing functions in less time than it is necessary to calculate the value of the function at one point. These requirements can met with a competent combination of well-known approaches in solving optimization problems and the specific specifics of the problem solved. When setting and solving such problems, the correct use of classical and modern methods solving continuous optimization problems is required, as well as knowledge of the features of applying these methods in optimization problems that arise in machine learning. The obtained processor circuits for the implementation of calculations are scratch-pad memory registers covered by delayed feedback, the signals of which summed in the initial cell. The prospects of PFRP as solving systems of linear algebraic equations tool by gradient methods shown. The possibility of using the PFRP for modeling the systems of the described SLAE, as well as possibility of solving the PFRP of a linear programming problem, also established.