In this manuscript, we consider smooth multi-objective optimization problems with convex constraints. We propose an extension of a augmented Lagrangian Method from recent literature. The new algorithm is specifically designed to handle sets points and produce good approximations the whole Pareto front, as opposed original one which converges single solution. prove properties global convergence ...

We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves sequence of inner subproblems which can be enforced to strongly convex and therefore admit unique solution. The resulting steps are shown equivalent inexact point iterations extended-real-valued cost function, allows for fairly simple analysis where convergence s...

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augm...

We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formul...

We consider global convergence properties of the augmented Lagrangian methods on problems with degenerate constraints, with a special emphasis on mathematical programs with complementarity constraints (MPCC). In the general case, we show convergence to stationary points of the problem under an error bound condition for the feasible set (which is weaker than constraint qualifications), assuming ...