A New Decomposition Method in Nonconvex Programming Via a Separable Augmented Lagrangian

Hamdi, Abdelouahed; Mahey, Philippe; Dussault, Jean-Pièrre

doi:10.1007/978-3-642-59073-3_7

Cited by 19 publications

(17 citation statements)

References 15 publications

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“…Different algorithms have been developed throughout the years (Watanabe and Ntshimura, 1978;Tappenden et al, 2015;Powell, 1969;Hamdi and Al-saud, 2008;Hamdi, 2005;Hamdi et al, 1997), which present different approaches to decompose the original problem and coordinate the solution. In this paper the algorithm used follows from the Separable Augmented Lagrangian Algorithm (SALA) family of methods (Hamdi et al, 1997;Hamdi, 2005;Hamdi and Al-saud, 2008). Reviews on different augmented Lagrangian decomposition methods can be found in Hamdi et al (1997); Tosserams et al (2009).…”

Section: Augmented Lagrangian Decomposition Methodsmentioning

confidence: 99%

Automated structure detection for distributed process optimization

Rio‐Chanona

Fiorelli

Vassiliadis

2016

Computers & Chemical Engineering

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The design and control of large-scale engineering systems, consisting of a number of interacting subsystems, is a heavily researched topic with relevance both for industry and academia. This paper presents two methodologies for optimal model-based decomposition, where an optimization problem is decomposed into several smaller sub-problems and subsequently solved by augmented Lagrangian decomposition methods. Largescale and highly nonlinear problems commonly arise in process optimization, and could greatly benefit from these approaches, as they reduce the storage requirements and computational costs for global optimization. The strategy presented translates the problem into a constraint graph. The first approach uses a heuristic community detection algorithm to identify highly connected clusters in the optimization problem graph representation. The second approach uses a multilevel graph bisection algorithm to find the optimal partition, given a desired number of sub-problems. The partitioned graphs are translated back into decomposed sets of sub-problems with a minimal number of coupling constraints. Results show both of these methods can be used as efficient frameworks to decompose optimization problems in linear time, in comparison to traditional methods which require polynomial time.

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Section: Augmented Lagrangian Decomposition Methodsmentioning

confidence: 99%

Automated structure detection for distributed process optimization

Rio‐Chanona

Fiorelli

Vassiliadis

2016

Computers & Chemical Engineering

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“…To build our new decomposition algorithm, we follow the well-known resources allocation scheme. Since we aim to develop an algorithm to decompose large scale, structured optimization models, we thought about the iterative approach studied and developed by Hamdi et al (1997), Hamdi (2005b), and Hamdi and Mishra (2011), the Separable Augmented Lagrangian Algorithm (SALA). To this goal, allocation vectors…”

Section: New Hdamentioning

confidence: 99%

“…This again motivated us to re-launch the use of the new hyperbolic functional (Xavier, 2001), which is twice continuously differentiable and is combining features of both exterior and interior penalty methods. Our approach consists in mixing the hyperbolic penalty algorithmic scheme with some recent decomposition algorithms developed by Hamdi et al (1997), Hamdi and Mahey (2000) and Hamdi (2005aHamdi ( , 2005b. These decomposition class of methods known as separable augmented Lagrangian algorithms (SALA) can be derived from the resource directive sub-problems associated with the coupling constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The paper is based upon the idea originally discussed by Hamdi et al (1997), where the authors proposed a decomposable scheme that overcame the non-separability of the obtained augmented Lagrangian function. But here, we limit ourselves to propose a primal method based on the hyperbolic penalty functional far from augmented lagrangians where we have separable penalized subproblems.…”

Section: Introductionmentioning

confidence: 99%

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A hyperbolic penalty method to solve structured convex minimization problems

al.¹

2020

Int. j. adv. appl. sci.

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This paper presents a decomposition algorithm based on the smooth hyperbolic penalty, which leads to a scheme suitable for parallelized computations. The proposed algorithm can be seen as a separable version of the earlier hyperbolic penalty method built, and its main idea is related to a penalty-type scheme mixed with a kind of resource allocation approach to decompose large scale separable constrained minimization programs.

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“…For instance, it is well-known that the rate of convergence of the Douglas-Rachford method is highly sensitive to the choice of the parameter introduced in the proximal step. More worrying is the fact that the control of the rate of the primal and dual sequences are conflicting, thus limiting the best expected linear rate of convergence to the value 0.5 and provoking nasty spiralling effects (see [30,45]). …”

Section: Introductionmentioning

confidence: 99%

A survey on operator splitting and decomposition of convex programs

Lenoir

Mahey

2016

RAIRO-Oper. Res.

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To cite this version:Philippe Mahey, Arnaud Lenoir. A survey on operator splitting and decomposition of convex programs. RAIRO -Operations Research, EDP Sciences, 2017, 51 (1) Abstract Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity of these algorithms with respect to the scaling parameters that drive the regularizing terms, in order to accelerate convergence rates for different classes of models.

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A New Decomposition Method in Nonconvex Programming Via a Separable Augmented Lagrangian

Cited by 19 publications

References 15 publications

Automated structure detection for distributed process optimization

Automated structure detection for distributed process optimization

A hyperbolic penalty method to solve structured convex minimization problems

A survey on operator splitting and decomposition of convex programs

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