A multifactor problem of non-linear programming with a decreasing input function

The continuous analogue of a multifactor non-linear problem of mathematical programming of high dimensionality with a decreasing input function is considered; the problem arises when devising optimal plans for joint production of one type of product and several types of auxiliary equipment. The problem is solved by using decomposition algorithms based on the structure of the set of solutions of subproblems. The conditions for a solution and set of solution to exist are obtained, together with efficient methods for devising optimal plans.