Researches On The Optimum Managing Program And Economic Equilibration Solutions For A Class Of Nonlinear System

Under the background of an enterprise production based on the shifting from the raw material bundles to the output bundles, a class of nonlinear type (with restriction) manufacturing system, whose solutions of economic balance and optimum managing programs are initially researched by applying some of nonlinear analysis methods, is introduced in this paper. As a result, some main theorems are obtained and the corresponding explanations are given out.Firstly, according to the rule of equilibrations between the supplying and the demanding, a kind of nonlinear input-output equation restricted is built up and tackled by the Brouwer degree theory and set-valued analysis approaches, from which some solvability (namely, existentiality and continuity) results are gained relevantly.Secondly, considering the variety of system managing strategies, we can extend a nonlinear restricted equation into a set-valued type input-output one with restriction, solvability(namely, existentiality and continuity) problems of which are given a primary try thanks to some theorems of zero point existence and homotopic correspondences belonging to nonlinear analysis. Therefore, some according solvability theorems are acquired.Lastly, we apply such Kuhn-Tucker theorem and subdifferntial idea as are usually used in nonlinear analysis science to the optimum managing tactics of system which will lead to the largest profit that the producer expects to earn, satisfying to it that pure outputs are not more than anticipated demands on the markets. From this, we give out some main results including the methods of decision to the optimum managing programs of system and the properties of the optimum managing strategy set affected by the price vector that make a certain economic sense.