For a given iterate generated by the augmented Lagrangian or the Lagrangian relaxation based method, we derive estimates for the distance to the primal solution of the underlying optimization problem. The estimates are obtained using some recent contributions to the sensitivity theory, under appropriate first or second order sufficient optimality conditions. The given estimates hold in situatio...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...

for all x ∈ IR, λ ∈ IR, μ ∈ IR +. PHR-based Augmented Lagrangian methods for solving (1) are based on the iterative (approximate) minimization of Lρ with respect to x ∈ Ω, followed by the updating of the penalty parameter ρ and the Lagrange multipliers approximations λ and μ. The most popular practical Augmented Lagrangian method gave rise to the Lancelot package [24, 25, 26]. Lancelot does not...

We study a class of methods for solving convex programs, which are based on nonquadratic Augmented Lagrangians for which the penalty parameters are functions of the multipliers. This gives rise to lagrangians which are nonlinear in the multipliers. Each augmented lagrangian is speciied by a choice of a penalty function ' and a penalty-updating function. The requirements on ' are mild, and allow...

For design optimization tasks, quite often a so-called one-shot approach is used. It augments the solution of the state equation with a suitable adjoint solver yielding approximate reduced derivatives that can be used in an optimization iteration to change the design. The coordination of these three iterative processes is well established when only the state equation is considered as equality c...

This paper is devoted to the numerical resolution of unit-commitment problems, with emphasis on the French model optimizing the daily production of electricity. The solution process has two phases. First a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. We then propose to use the latter in the second phase, for a heuristic resolution based o...

The alternating direction method of multipliers (ADMM) is commonly used for distributed model fitting problems, but its performance and reliability depend strongly on userdefined penalty parameters. We study distributed ADMM methods that boost performance by using different fine-tuned algorithm parameters on each worker node. We present a O(1/k) convergence rate for adaptive ADMM methods with n...

In remote sensing images, the common existing stripe noise always severely affects the imaging quality and limits the related subsequent application, especially when it is with high density. To well process the dense striped data and ensure a reliable solution, we construct a statistical property based constraint in our proposed model and use it to control the whole destriping process. The alte...

We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vectorand matrixvalued functions on parametric surfaces. We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a...

The nuclear norm is widely used to induce low-rank solutions for many optimization problems with matrix variables. Recently, it has been shown that the augmented Lagrangian method (ALM) and the alternating direction method (ADM) are very efficient for many convex programming problems arising from various applications, provided that the resulting subproblems are sufficiently simple to have close...