A neural networks approach to inverse optimization problems with nonstandard quadratic criterion functions

Abstract

Proposed in this paper is a novel neural networks approach to inverse optimization problems with nonstandard quadratic criterion functions. An inverse optimization problem here means to obtain a positive semidefinite quadratic criterion function which makes a given solution optimal under given constraint conditions. However, in contrast to the case of standard quadratic criterion functions, a cruterion function cannot be determined uniquely even when there is only one active constraint condition. To solve this difficulty, it is proposed to obtain a criterion function closest to the studard quadratic criterion function. For this purpose, the sum of the absolute values of off-diagonal connection weights and that of squares of them are used as indicators for the distance from the standard quadratic criterion function. A structural learning with forgetting applied to off diagonal connection weights successfully generates a simplified quadratic criterion function. How criterion parameters and Lagarange multipliers changes for various gradient vectors is also analyzed.