Parameter Selection with Inverse Optimization

Abstract

An inverse optimization program is about inferring the parameters for a forward optimization program. The easiest inverse optimization model is that for a linear forward optimization program. Given a desired target x?, the inverse problem aims to solve for a cost vector c such that the optimal solution of the forward program coincides with x?. This is equivalent to ?nd the dual-cost pair (p, c) satisfying strong duality and dual feasibility. The objective of an inverse problem can be written as the least squares of the discrepancies of the cost vector c. The research on inverse optimization can be traced back to the inverse shortest path problems. Later on, the inverse optimization model and method for the forward linear program has been extended to integer programming, mixed integer programming, convex programming, and multi-objective linear optimization. In this research we aim at furthering the analytical technology with the method of inverse optimization as a basis for the ef?cient use of data in terms of robust forecasting and optimal decision making. Keywords: inverse optimization, parameter selection, data analytics