 ##  [Primal–Dual Relationship](/primal-dual-relationship) 

  ##  [Primal–Dual Relationship](https://mathlogic.quantumdictionary.io/primal-dual-relationship-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The mathematical relationship between a primary (primal) formulation and its associated dual formulation that links optimality conditions, Lagrange multipliers or conjugate variables, and often yields bounds, sensitivity information, or alternative algorithms.