A Solution to Static Inverse Optimization Problems with Quadratic Constraints
by Learning of Neural Networks

Abstract

In this paper we propose a novel approach to static inverse optimization problems with quadratic constraints by learning of neural networks for interpreting real-world data. This proposal has an advantage in that marginal rates of substitution change smoothly in contrast to the case of static inverse optimization with linear constraints. Based on this characteristic, more accurate interpretation of data by static inverse optimization becomes possible. To evaluate the effectiveness of the proposed method, we solve static inverse optimization problems with quadratic constraints using artificial data. We also propose a method to generate quadratic constraints from given data.