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Renato Monteiro

Publications and source records attributed to Renato Monteiro.

4 recordsLinked to original sources
arXiv2026

Dimension-Free Complexity Guarantees for Dual Dynamic Programming

This paper studies the complexity of a dual dynamic programming (DDP) method for solving a class of convex optimization problems with linear coupling constraints. Existing complexity results based on DDP depend on the dimensions of the state vectors and, in particular, grow exponentially with dimension. The goal of this paper is to establish a complexity bound that is independent of the dimension. Our approach first studies an unconstrained strongly convex problem and develops a flexible framework for DDP, called FDDP, for solving the associated dynamic programming equations, and establishes an iteration-complexity bound for it that is independent of the dimension. A dimension-independent complexity bound for the original linearly constrained problem is then obtained by applying FDDP to a corresponding unconstrained strongly convex problem obtained via smoothing and penalization. Inspired by the literature on bundle methods, FDDP updates lower approximations of cost-to-go functions through a generic procedure that includes both the classical multi-cut DDP and a new two-cut DDP variant as special cases. The two-cut variant maintains only two affine cuts per stage at each iteration, making it more memory-efficient while retaining the same theoretical guarantees. Finally, numerical experiments illustrate the practical behavior of multi-cut and two-cut DDP, including their dependence on problem parameters and their performance relative to a direct quadratic constraint reformulation.

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arXiv2021

Stochastic Dynamic Cutting Plane for multistage stochastic convex programs

We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower affine functions not only for the cost-to-go functions, as SDDP does, but also for some or all nonlinear cost and constraint functions. We show the almost sure convergence of StoDCuP. We also introduce an inexact variant of StoDCuP where all subproblems are solved approximately (with bounded errors) and show the almost sure convergence of this variant for vanishing errors.

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arXiv2021

Inexact cuts in SDDP applied to multistage stochastic nondifferentiable problems

In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP) called ISDDP was introduced which uses approximate (instead of exact with SDDP) primal dual solutions of the problems solved in the forward and backward passes of the method. That variant of SDDP was studied in [13] for linear and for differentiable nonlinear Multistage Stochastic Programs (MSPs). In this paper, we extend ISDDP to nondifferentiable MSPs. We first provide formulas for inexact cuts for value functions of convex nondifferentiable optimization problems. We then combine these cuts with SDDP to describe ISDDP for nondifferentiable MSPs and analyze the convergence of the method. More precisely, for a problem with T stages, we show that for errors bounded from above by epsilon, the limit superior and limit inferior of sequences of upper and lower bounds on the optimal value of the problem are at most at distance 3*epsilon*T to the optimal value and that for asymptotically vanishing errors ISDDP converges to an optimal policy. [13] V. Guigues, Inexact cuts in Stochastic Dual Dynamic Programming, Siam Journal on Optimization, 30(1), 407-438, 2020.

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