Auxiliary problem principle and decomposition of optimization problems

1980 ◽  
Vol 32 (3) ◽  
pp. 277-305 ◽  
Author(s):  
G. Cohen
Keyword(s):  
Optimization Problems ◽  
Auxiliary Problem ◽  
Auxiliary Problem Principle

scholarly journals Decentralized Voltage Optimization Based on the Auxiliary Problem Principle in Distribution Networks with DERs

2021 ◽  
Vol 11 (10) ◽  
pp. 4509
Author(s):  
Anna Rita Di Fazio ◽  
Chiara Risi ◽  
Mario Russo ◽  
Michele De Santis
Keyword(s):  
Distribution Systems ◽  
Auxiliary Problem ◽  
Optimization Procedure ◽  
Distribution Networks ◽  
Small Dimension ◽  
Quadratic Program ◽  
Voltage Profile ◽  
Distributed Energy ◽  
Auxiliary Problem Principle ◽  
Coordination Process

This paper addresses the problem of optimizing the voltage profile of radially-operated distribution systems by acting on the active and reactive powers provided by distributed energy resources (DERs). A novel voltage optimization procedure is proposed by adopting a decentralized control strategy. To this aim, a centralized voltage optimization problem (VOP), minimizing the distance of all the nodal voltages from their reference values, is firstly formulated as a strictly-convex quadratic program. Then, the centralized VOP is rewritten by partitioning the network into voltage control zones (VCZs) with pilot nodes. To overcome the lack of strictly convexity determined by the reduction to the pilot nodes, the dual centralized VOP working on the augmented Lagrangian function is reformulated and iteratively solved by the method of multipliers. Finally, a fully-distributed VOP solution is obtained by applying a distributed algorithm based on the auxiliary problem principle, which allows for solving in each VCZ a quadratic programming problem of small dimension and to drive the VCZ solutions toward the overall optimum by an iterative coordination process that requires to exchange among the VCZs only scalar values. The effectiveness and feasibility of the proposed method have been demonstrated via numerical tests on the IEEE 123-bus system.

Shape Sensitivity Analysis Applied to Exterior Acoustics

2001 ◽  
Author(s):  
Gonzalo R. Feijóo ◽  
Assad A. Oberai ◽  
Peter M. Pinsky
Keyword(s):  
Optimization Problems ◽  
Auxiliary Problem ◽  
Adjoint Problem ◽  
The Body ◽  
Structural Acoustics ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Primal Problem ◽  
Acoustic Media ◽  
The Cost

Abstract We present a method to calculate the derivative of a functional that depends on the shape of a body immersed in an acoustic media. The functional depends implicitly on the shape through the solution of an exterior acoustic problem. The derivative is calculated in terms of the solution of the primal problem and an auxiliary problem, the adjoint problem. An important aspect of this method is that the cost of calculating the derivative is independent of the number of parameters used to represent the shape of the body. This allows for efficient solution of optimization problems in structural acoustics.

Extended auxiliary problem principle using Bregman distances

Optimization ◽  
2004 ◽  
Vol 53 (5-6) ◽  
pp. 603-623 ◽  
Author(s):  
A. Kaplan ◽  
R. Tichatschke
Keyword(s):  
Auxiliary Problem ◽  
Bregman Distances ◽  
Auxiliary Problem Principle

scholarly journals A Predictor-Corrector Method for Solving Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zong-Ke Bao ◽  
Ming Huang ◽  
Xi-Qiang Xia
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
The Other ◽  
Stationary Points ◽  
Stopping Criterion ◽  
Auxiliary Problem Principle ◽  
One Step ◽  
Predictor Corrector

We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise toΔ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

Sign in / Sign up

Export Citation Format

Share Document