a neural network framework for solving inverse optimal value problem: cost efficiency point of view

This study presents a new bi-level inverse optimal value model whichextends the classical inverse optimal value problem to include cost efficiency . this newbi-level inverse model affords novel insights into the managers dealing with the inversedea problem and the cost efficiency simultaneously in a hierarchical structure . usingthe karush-kuhn-tucker (kkt) conditions , the bi-level inverse model is reduced to aone-level mathematical program with complementarity constraints (mpcc) . accordingto optimization theory and some concepts of ordinary differential equations , a recurrentneural network is developed for solving this one-level mathematical programmingproblem. under a proper assumption and utilizing a suitable lyapunov function, it isshown that the proposed neural network is lyapunov stable and convergent to an exactoptimal solution of the original problem. finally, an illustrative example is elaborated tosubstantiate the applicability and effectiveness of the proposed approach.