Duality in Convex Optimization
A convex optimization problem can be paired with a dual problem involving the conjugates of the functions appearing it its (primal) formulation. In this chapter, we study the interplay between primal and dual problems in the context of Fenchel–Rockafellar duality and, more generally, for bivariate functions. The latter approach leads naturally to saddle points and Lagrangians. Special attention is given to minimization under equality constraints and under inequality constraints. We start with a discussion of instances in which all primal solutions can be recovered from an arbitrary dual solution.
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