Interpretation of real data by static inverse optimization with quadratic constraints

We propose a novel approach to static inverse optimization with quadratic constraints by learning of neural networks. The use of quadratic constraints has two advantages for interpreting data. One is that quadratic constraints can reflect statistical characteristics of given data. The other is that the degeneration does not occur, even if the number of active constraints is only one. Based on these characteristics, more accurate interpretation of data becomes possible by static inverse optimization with quadratic constraints. Applications of the proposed method to rented housing data (about 5000 samples with 4 attributes) well demonstrate its effectiveness. Criterion functions for deciding housing of tenants living along Yamanote and Soubu-Chuo lines in Tokyo are successfully estimated.