arXiv subjects

Olivier Bilenne

Publications and source records attributed to Olivier Bilenne.

6 recordsLinked to original sources

arXiv2026

An Exact Method for a Problem of Time Slot Pricing

A company provides a service at different time slots, each slot being endowed with a capacity. A non-atomic population of users is willing to purchase this service. The population is modeled as a continuous measure over the preferred times. Every user looks at the time slot that minimizes the sum of the price assigned by the company to this time slot and the distance to their preferred time. If this sum is non-negative, then the user chooses this time slot for getting the service. If this sum is positive, then the user rejects the service. We address the problem of finding prices that ensure that the volume of users choosing each time slot is below capacity, while maximizing the revenue of the company. For the case where the distance function is convex, we propose an exact algorithm for solving this problem in time $O(n^3|P|^3)$, where $P$ is the set of possible prices and $n$ is the number of time slots. For the case where the prices can be any real numbers, this algorithm can also be used to find asymptotically optimal solutions in polynomial time under mild extra assumptions on the distance function and the measure modeling the population.

math.OC↗

arXiv2024

Parametrization and convergence of a primal-dual block-coordinate approach to linearly-constrained nonsmooth optimization

This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual algorithm, based on inexact proximal gradient steps. A specificity of the considered algorithm is its robustness, as it converges even in the absence of strong duality or when the linear program is inconsistent. Using matrix preconditiong, we derive tight sublinear convergence rates with and without duality assumptions and for both the convex and the strongly convex settings. Our developments are extensions and particularizations of original algorithms proposed by Malitsky (2019) and Luke and Malitsky (2018). Numerical experiments are provided for an optimal transport problem of service pricing.

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arXiv2022

A privacy-preserving distributed computational approach for distributed locational marginal prices

An important issue in today's electricity markets is the management of flexibilities offered by new practices, such as smart home appliances or electric vehicles. By inducing changes in the behavior of residential electric utilities, demand response (DR) seeks to adjust the demand of power to the supply for increased grid stability and better integration of renewable energies. A key role in DR is played by emergent independent entities called load aggregators (LAs). We develop a new decentralized algorithm to solve a convex relaxation of the classical Alternative Current Optimal Power Flow (ACOPF) problem, which relies on local information only. Each computational step can be performed in an entirely privacy-preserving manner, and system-wide coordination is achieved via node-specific distribution locational marginal prices (DLMPs). We demonstrate the efficiency of our approach on a 15-bus radial distribution network.

eess.SY↗

arXiv2021

Dispatching to Parallel Servers: Solutions of Poisson's Equation for First-Policy Improvement

Policy iteration techniques for multiple-server dispatching rely on the computation of value functions. In this context, we consider the continuous-space M/G/1-FCFS queue endowed with an arbitrarily-designed cost function for the waiting times of the incoming jobs. The associated relative value function is a solution of Poisson's equation for Markov chains, which in this work we solve in the Laplace transform domain by considering an ancillary, underlying stochastic process extended to (imaginary) negative backlog states. This construction enables us to issue closed-form relative value functions for polynomial and exponential cost functions and for piecewise compositions of the latter, in turn permitting the derivation of interval bounds for the relative value function in the form of power series or trigonometric sums. We review various cost approximation schemes and assess the convergence of the interval bounds these induce on the relative value function. Namely: Taylor expansions (divergent, except for a narrow class of entire functions with low orders of growth), and uniform approximation schemes (polynomials, trigonometric), which achieve optimal convergence rates over finite intervals. This study addresses all the steps to implementing dispatching policies for systems of parallel servers, from the specification of general cost functions towards the computation of interval bounds for the relative value functions and the exact implementation of the first-policy improvement step.

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arXiv2020

Fast Optimization with Zeroth-Order Feedback in Distributed, Multi-User MIMO Systems

In this paper, we develop a gradient-free optimization methodology for efficient resource allocation in Gaussian MIMO multiple access channels. Our approach combines two main ingredients: (i) an entropic semidefinite optimization based on matrix exponential learning (MXL); and (ii) a one-shot gradient estimator which achieves low variance through the reuse of past information. This novel algorithm, which we call gradient-free MXL algorithm with callbacks (MXL0$^{+}$), retains the convergence speed of gradient-based methods while requiring minimal feedback per iteration$-$a single scalar. In more detail, in a MIMO multiple access channel with $K$ users and $M$ transmit antennas per user, the MXL0$^{+}$ algorithm achieves $ε$-optimality within $\text{poly}(K,M)/ε^2$ iterations (on average and with high probability), even when implemented in a fully distributed, asynchronous manner. For cross-validation, we also perform a series of numerical experiments in medium- to large-scale MIMO networks under realistic channel conditions. Throughout our experiments, the performance of MXL0$^{+}$ matches$-$and sometimes exceeds$-$that of gradient-based MXL methods, all the while operating with a vastly reduced communication overhead. In view of these findings, the MXL0$^{+}$ algorithm appears to be uniquely suited for distributed massive MIMO systems where gradient calculations can become prohibitively expensive.

cs.IT↗

arXiv2015

Asymptotic convergence rates for coordinate descent in polyhedral sets

We consider a family of parallel methods for constrained optimization based on projected gradient descents along individual coordinate directions. In the case of polyhedral feasible sets, local convergence towards a regular solution occurs unconstrained in a reduced space, allowing for the computation of tight asymptotic convergence rates by sensitivity analysis, this even when global convergence rates are unavailable or too conservative. We derive linear asymptotic rates of convergence in polyhedra for variants of the coordinate descent approach, including cyclic, synchronous, and random modes of implementation. Our results find application in stochastic optimization, and with recently proposed optimization algorithms based on Taylor approximations of the Newton step.

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