On efficiently solving the subproblems of a level-set method for fused lasso problems

In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890–912 and SIAM J. on Optimization, 21 (2011), pp.~1201–1229] to solve the fused lasso problems, one needs to solve a sequence of regularized least squares subproblems. In order to make the level-set method practical, we develop … Read more

Solving piecewise linear equations in abs-normal form

With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL … Read more

Local Convergence of the Method of Multipliers for Variational and Optimization Problems under the Sole Noncriticality Assumption

We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under the … Read more


This note suggests the implicit function theorem for generalized equations, unifying Robinson’s theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings. Article Download View STRONGLY REGULAR NONSMOOTH GENERALIZED EQUATIONS (REVISED)