On the Interpretation of Optimal Dual Solutions in Convex Programming

Abstract

The relationships between multiple optimal dual solutions of a convex programming problem and the corresponding primal optimal value function are established by straightforward arguments on known results in duality theory. The subsequent discussion includes a demonstration that one-sided shadow prices can be found by solving a linear programming problem, conditions for the uniqueness and validity of the classical shadow price interpretation and a specialization of the results to the linear programming case.

Keywords:

• convex programming
• linear programming
• optimal dual solutions
• shadow prices
• equilibrum prices