Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original problem.

This inverse problem can be written as a minimization problem with second-order cone complementarity constraints and a positive semidefinite cone constraint. Applying the duality theory, we ...

Marshall, Paul W. "Linear Programming: A Technique for Analyzing Resource Allocation Problems." Harvard Business School Background Note 171-322, January 1971. (Revised November 1975 ...