Proximal-ACCPM: A Versatile Oracle Based Optimisation Method

Babonneau, Frédéric Louis François; Beltrán, César; Haurie, Alain; Tadonki, Claude; Vial, Jean–Philippe

doi:10.1007/3-540-36626-1_4

Cited by 25 publications

(33 citation statements)

References 21 publications

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“…Indeed the nondifferentable convex optimization problem could be also solved using other methods. However as reported in [25] ACCPM works efficiently on several instances of large scale optimization problems which could be tackled through a formulation as a nondifferentiable convex optimization. An interesting advantage offered by ACCPM-PI, in this particular control application, was to allow the use of policy improvement techniques to solve the subproblems at the oracle level.…”

Section: Discussionmentioning

confidence: 99%

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Haurie

Moresino

2007

IEEE Trans. Automat. Contr.

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This paper deals with a class of ergodic control problems for systems described by Markov chains with strong and weak interactions. These systems are composed of a set of m subchains that are weakly coupled. Using results already available in the literature one formulates a limit control problem the solution of which can be obtained via an associated nondifferentiable convex programming (NDCP) problem. The technique used to solve the NDCP problem is the Analytic Center Cutting Plane Method (ACCPM) which implements a dialogue between, on one hand, a master program computing the analytical center of a localization set containing the solution and, on the other hand, an oracle proposing cutting planes that reduce the size of the localization set at each main iteration. The interesting aspect of this implementation comes from two characteristics: (i) the oracle proposes cutting planes by solving reduced sized Markov Decision Problems (MDP) via a linear programm (LP) or a policy iteration method; (ii) several cutting planes can be proposed simultaneously through a parallel implementation on m processors. The paper concentrates on these two aspects and shows, on a large scale MDP obtained from the numerical approximation "à la Kushner-Dupuis" of a singularly perturbed hybrid stochastic control problem, the important computational speed-up obtained.

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Section: Discussionmentioning

confidence: 99%

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Haurie

Moresino

2007

IEEE Trans. Automat. Contr.

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“…The equations of the model are listed below, note that t represents the integer value of the time index, not the real value of time, which is discretised in 10-year steps. The model maximizes the sum of the discounted welfare (or utility of consumption) W (c(t), L(t)) over all the periods as shown in equations (1)- (2). When α = 1, the utility function takes the form L log(c):…”

Section: The Economy Modelmentioning

confidence: 99%

“…In this section, we recall the basic features of the oracle-based optimisation (OBO) procedure as described in [2]. The convex optimisation problem (29) belongs to the class of problems that can be solved through an OBO technique: the hypograph of U (X) (defined as {(X, z) ∈ R n+1 | z ≤ U (X)}) and the feasible set can be delineated by a polyhedral outer approximation.…”

Section: The Proximal-accpm Algorithmmentioning

confidence: 99%

“…This polyhedral set corresponds to a superset of the linear outer approximation of the hypograph of U and contains the optimal solution X * and the associated objective value U * = z * . Proximal-ACCPM, specifically its query point generator module, chooses the next pointX k+1 as the analytic center of L k (see [2] for a definition of this concept and the Newton procedure to calculate it). The procedure calls the oracle with the new point and generates one or several new cuts.…”

Section: The Proximal-accpm Algorithmmentioning

confidence: 99%

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Coupling climate and economic models in a cost-benefit framework: A convex optimisation approach

Drouet

Edwards

Haurie

2006

Environ Model Assess

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In this paper we present a general method, based on a convex optimisation technique, that facilitates the coupling of climate and economic models in a cost-benefit framework. As a demonstration of the method, we couple an economic growth model a la Ramsey adapted from DICE-99 with an efficient intermediate complexity climate model, C-GOLDSTEIN, which has highly simplified physics, but fully 3-D ocean dynamics. As in DICE-99 we assume that an economic cost is associated with global temperature change: this change is obtained from the climate model which is driven by the GHG concentrations computed from the economic growth path. The work extends a previous paper in which these models were coupled in cost-effectiveness mode. Here we consider the more intricate cost-benefit coupling in which the climate impact is not fixed a priori. We implement the coupled model using an oracle-based optimisation technique. Each model is contained in an oracle which supplies model output and information on its sensitivity to a master program. The algorithm Proximal-ACCPM guarantees the convergence of the procedure under sufficient convexity assumptions. Our results demonstrate the possibility of a consistent, cost-benefit, climate-damage optimisation analysis with a 3-D climate model.

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“…The use of stabilization terms within the ACCPM has been successful, as shown in Babonneau et al (2007).…”

Section: Variants Of the Standard Column Generation Methodsmentioning

confidence: 93%

Theoretical and computational issues for improving the performance of linear optimization methods

Munari¹,

Augusto²

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Proximal-ACCPM: A Versatile Oracle Based Optimisation Method

Cited by 25 publications

References 21 publications

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Coupling climate and economic models in a cost-benefit framework: A convex optimisation approach

Theoretical and computational issues for improving the performance of linear optimization methods

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