solving inverse optimization problems in linear programming: a geometric and algorithmic approach

This paper addresses the inverse optimization problem for linear programming, focusing on determining a cost vector that ensures a pre-specified solution is optimal. two approaches are presented: (i) using the karush-kuhn-tucker (kkt) conditions, and (ii) a geometric perspective leveraging first-order necessary conditions. the latter method results in a convex quadratic programming problem, solved efficiently using the gradient projection method. numerical experiments, including a complex resource allocation problem, validate the proposed approach. this study extends the theory and application of inverse optimization across logistics, resource management, and supply chain optimization.