A Primal-Dual Algorithm for Minimizing a Non-Convex Function Subject to Bound and Linear Equality Constraints

A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to simple bounds and linear equality constraints. The method alternates between a classical primal-dual step and a Newton-like step in order to ensure descent on a suitable merit function. Convergence of a well-defined subsequene of iterates is proved from arbitrary starting points. Algorithmic variants are discussed and preliminary numerical results presented.