Exact penalty functions with multidimensional penalty parameter and adaptive penalty updates

Adaptive ADMM with Spectral Penalty Parameter Selection

The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is highly sensitive to a penalty parameter, which makes ADMM often unreliable and hard to automate for a non-expert user. We tackle this weakness of ADMM by proposin...

Penalty Functions

Exact Penalty Principle∗

Exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most of results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem and the reverse property is rarely stud...

Exact Penalty Methods

Exact penalty methods for the solution of constrained optimization problems are based on the construction of a function whose unconstrained minimizing points are also solution of the constrained problem. In the rst part of this paper we recall some deenitions concerning exactness properties of penalty functions, of barrier functions, of augmented Lagrangian functions, and discuss under which as...

Decrease of the Penalty Parameter in Differentiable Penalty Function Methods

We propose a simple modification to the differentiable penalty methods for solving nonlinear programming problems. This modification decreases the penalty parameter and the ill-conditioning of the penalty method and leads to a faster convergence to the optimal solution. We extend the modification to the augmented Lagrangian method and report some numerical results on several nonlinear programmi...