With respect to the below question.
I am currently building a similar econometric model for menu prices optimization for a restaurant in a country. This is a multivariate model which studies the interactions between different items and their prices to produce a sales output for one specific item from the menu. Currently, I have been using a linear regression model combined with linear optimization to optimize profit by varying prices.
I aim to move towards a more econometric model and as suggested in the question non-linear programming seems the best route.
Although program everything through python, I would want to grasp the mathematics behind creating a robust multi-layered non-linear model. Could you suggest books or resources that would help me out on this.