SDDP for multistage stochastic linear programs based on spectral risk measures

Guigues, Vincent; Römisch, Werner

doi:10.1016/j.orl.2012.04.006

Cited by 23 publications

(18 citation statements)

References 19 publications

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“…As a result, ξ [6] = (ξ 5 , ξ 6 ). Reasoning similarly and going backward in time, we obtain ξ [5] = (ξ 4 , ξ 5 ) and ξ [4] = (ξ 2 , ξ 3 , ξ 4 ). ξ [7] = (ξ 5 , ξ 6 , ξ 7 ) Figure 1.…”

Section: Sddp For a Class Of Non-risk-averse Interstage Dependent Stomentioning

confidence: 95%

“…Next, we consider a risk-averse formulation of (1) using a multiperiod risk measure proposed in [4], [5] that allows us to apply SDDP to approximate the corresponding risk-averse recourse functions. For the class of problems considered in this paper, we provide formulas for the cuts built in this risk-averse version of SDDP.…”

Section: Introductionmentioning

confidence: 99%

“…In the next section, devoted to numerical simulations, approximations of these risk-averse recourse functions are used on a real-life application with an affine process model. For this reason and for the sake of completeness, the cuts needed to obtain approximations of the risk-averse recourse functions using SDDP are derived in Theorem 3.1 5 Risk measures are defined on random variables representing costs, contrary to [4] where they are defined on random variables representing incomes. We easily switch from one setting to another since an income is the opposite of a cost.…”

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confidence: 99%

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SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Guigues

2013

Comput Optim Appl

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Abstract. We consider interstage dependent stochastic linear programs where both the random right-hand side and the model of the underlying stochastic process have a special structure. Namely, for equality constraints (resp. inequality constraints) the right-hand side is an affine function (resp. a given function bt) of the process value for the current time step t. As for m-th component of the process at time step t, it depends on previous values of the process through a function htm.For this type of problem, to obtain an approximate policy under some assumptions for functions bt and htm, we detail a stochastic dual dynamic programming algorithm. Our analysis includes some enhancements of this algorithm such as the definition of a state vector of minimal size, the computation of feasibility cuts without the assumption of relatively complete recourse, as well as efficient formulas for sharing optimality and feasibility cuts between nodes of the same stage. The algorithm is given for both a non-risk-averse and a risk-averse model. We finally provide preliminary results comparing the performances of the recourse functions corresponding to these two models for a real-life application.

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Section: Sddp For a Class Of Non-risk-averse Interstage Dependent Stomentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Guigues

2013

Comput Optim Appl

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“…Assumptions (H2-NL)-(a),(b),(c) in the nonlinear case imply the convexity of cost-to-go functions Q t (·, 1). The assumptions above also ensure (both in the linear and nonliner cases) that SDDP applied to dynamic programming equations (20), (21), (22) will converge, as long as samples in the forward passes are independent, see [38,17,14] for details.…”

Section: 2mentioning

confidence: 99%

Multistage Stochastic Programs with a Random Number of Stages: Dynamic Programming Equations, Solution Methods, and Application to Portfolio Selection

Guigues¹

2018

SSRN Journal

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We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and how to solve these equations using the Stochastic Dual Dynamic Programming algorithm. Finally, we consider a portfolio selection problem over an optimization period of random duration. For several instances of this problem, we show the gain obtained using a policy that takes the randomness of the number of stages into account over a policy built taking a fixed number of stages (namely the maximal possible number of stages).

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“…Since many real-life applications in, e.g., finance and engineering, can be modelled by such problems, until recently most papers on SDDP and related decomposition methods, including theory papers, focused on enhancements of the method for MSLPs. These enhancements include risk-averse SDDP [16], [9] [8], [14], [11], [17] and a convergence proof of SDDP in [15] and of variants incorporating cut selection in [7].…”

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confidence: 99%

Inexact Cuts in Stochastic Dual Dynamic Programming

Guigues¹

2020

SIAM J. Optim.

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We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of the method are solved with bounded errors (inexactly). This inexact variant of SDDP is described both for linear problems (the corresponding variant being denoted by ISDDP-LP) and nonlinear problems (the corresponding variant being denoted by ISDDP-NLP). We prove convergence theorems for ISDDP-LP and ISDDP-NLP both for bounded and asymptotically vanishing errors. Finally, we present the results of numerical experiments comparing SDDP and ISDDP-LP on a portfolio problem with direct transaction costs modelled as a multistage stochastic linear optimization problem. On these experiments, ISDDP-LP allows us to obtain a good policy faster than SDDP.

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SDDP for multistage stochastic linear programs based on spectral risk measures

Cited by 23 publications

References 19 publications

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Multistage Stochastic Programs with a Random Number of Stages: Dynamic Programming Equations, Solution Methods, and Application to Portfolio Selection

Inexact Cuts in Stochastic Dual Dynamic Programming

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