An iterative solver-based long-step infeasible primal-dual path-following algorithm for convex QP based on a class of preconditioners

Lu, Zhaosong; Monteiro, Renato D. C.; O'Neal, Jerome W.

doi:10.1080/10556780802414049

Cited by 3 publications

(4 citation statements)

References 28 publications

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“…If no iteration of the while loop is necessary we have 1 (l) which is less than δ i (1 − η)/ ∆z i,(l) , then the loop terminates. Thus, (37) holds.…”

Section: Fundingmentioning

confidence: 94%

“…The approach presented in the latter paper falls in the class of inexact interior-point methods which have been studied thoroughly over the past two decades, e.g. see [3,23,38,31,35,17,4,51,8,7,49,37,1,14,15]. These methods combine primal or primal-dual interior point methods with iterative algorithms for solving linear systems of equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A distributed primal-dual interior-point method for loosely coupled problems using ADMM

Annergren,

Pakazad,

Hansson

et al. 2014

Preprint

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In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-dual interior-point methods with the remarkable parallelizability of ADMM. The resulting algorithm has superior computational properties with respect to ADMM directly applied to our problem. The amount of computations that needs to be conducted by each computing agent is far less. In particular, the updates for all variables can be expressed in closed form, irrespective of the type of optimization problem. The most expensive computational burden of the algorithm occur in the updates of the primal variables and can be precomputed in each iteration of the interior-point method. We verify and compare our method to ADMM in numerical experiments.

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“…If no iteration of the while loop is necessary we have 1 (l) which is less than δ i (1 − η)/ ∆z i,(l) , then the loop terminates. Thus, (37) holds.…”

Section: Fundingmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

A distributed primal-dual interior-point method for loosely coupled problems using ADMM

Annergren,

Pakazad,

Hansson

et al. 2014

Preprint

View full text Add to dashboard Cite

show abstract

“…The operator employs quadratic approximations of the objective functions and constraints for the purpose of enhancing local search phase. Lu et al [18] present a long-step infeasible primal-dual path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of a preconditioned iterative linear…”

Section: Literature Reviewmentioning

confidence: 99%

On the Quadratic Transportation Problem

Adlakha

Kowalski²

2013

OJOp

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We present a direct analytical algorithm for solving transportation problems with quadratic function cost coefficients. The algorithm uses the concept of absolute points developed by the authors in earlier works. The versatility of the proposed algorithm is evidenced by the fact that quadratic functions are often used as approximations for other functions, as in, for example, regression analysis. As compared with the earlier international methods for quadratic transportation problem (QTP) which are based on the Lagrangian relaxation approach, the proposed algorithm helps to understand the structure of the QTP better and can guide in managerial decisions. We present a numerical example to illustrate the application of the proposed method.

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“…It allows the linear system to be solved to a low accuracy when the current iterate is far from the solution. In [13] the convergence analysis of inexact infeasible primal-dual path-following algorithm for convex quadratic programming is presented. In these papers the search directions are inexact as the PCG method is used to solve the normal equations.…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization

Al-Jeiroudi

Gondzio

2008

J Optim Theory Appl

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In this paper we present the convergence analysis of the inexact infeasible path-following (IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix.The KKT system is solved approximately. Therefore, it becomes necessary to study the convergence of interior point method for this specific inexact case. We present the convergence analysis of the inexact infeasible path-following (IIPF) algorithm, prove the global convergence of this method and provide complexity analysis.

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An iterative solver-based long-step infeasible primal-dual path-following algorithm for convex QP based on a class of preconditioners

Cited by 3 publications

References 28 publications

A distributed primal-dual interior-point method for loosely coupled problems using ADMM

A distributed primal-dual interior-point method for loosely coupled problems using ADMM

On the Quadratic Transportation Problem

Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization

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