Due to update the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practice, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often results in “too-small...

This paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. In fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. Thepower output of each hydro unit varies with the rate of water discha...

For nonconvex optimization problem with both equality and inequality constraints, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. New iterative strategy on penalty parameter is presented. Different global convergence properties are established depending on whether the penalty parameter is bounded. Even if the iterative sequence {xk} is diverg...

In this paper we present an adaptive strategy to obtain an incompressible wind field that adjusts to an experimental one, and verify boundary conditions of physical interest. We use an Augmented Lagrangian formulation for solving this problem. Our method is based on an Uzawa iteration to update the Lagrange multiplier and on an elliptic adaptive inner iteration for velocity. Several examples sh...

A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the n×n submatrix residing in the (1,1)block of the (n+m)×(n+m) augmented matrix that would generate non-expansive iterations in R. The classic multiplier me...

Recently, researchers have proposed decision support tool for generating suggestions for bids in combinatorial reverse auction based on disclosure of bids. An interesting issue is to design an effective mechanism to guide the bidders to collectively minimize the overall cost without explicitly disclosing the bids. We consider a winner determination problem for combinatorial reverse auction and ...

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to clos...

Abstract In this paper we will present a review of recent advances in the application augmented Lagrange multiplier method as general approach for generating multiplier-free stabilised methods. The Lagrangian consists standard by penalty term, penalising constraint equations, and is well known basis iterative algorithms constrained optimisation problems. Its use stabilisation methods computatio...

This paper presents a numerical study of a stochastic augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is...