Computing algorithms for solution of some problems in linear and linear integer programming. I

Multi-purpose computing algorithms for solution and optimization of control systems which proceed from sufficient conditions of optimality and whose core is an elementary operation of improving the function $\varphi(t,y)$ are used in investigation of mathematical programming problems: the general problem of linear programming with bilateral constraints; problems of assignment and allocation which are particular cases of the transport problem; and the traveling salesman problem. For the latter two types accurate solution algorithms are developed. This part describes general constructions in implementation of an elementary operation and the first of the above problems is investigated.