augmented lagrangian method

Smoothing Method of Multipliers for Sum-Max Problems

  • Michael Zibulevsky
    • Categories Convex Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , ,

    We study nonsmooth unconstrained optimization problem, which includes sum of pairwise maxima of smooth functions. Minimum $l_1$-norm approximation is a particular case of this problem. Combining ideas Lagrange multipliers with smooth approximation of max-type function, we obtain a new kind of nonquadratic augmented Lagrangian. Our approach does not require artificial variables, and preserves sparse structure … Read more

    A practical general approximation criterion for methods of multipliers based on Bregman distances

  • Jonathan Eckstein
    • Categories Convex Optimization Tags , , ,

    This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels — including the classical quadratic method of multipliers — the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or … Read more