This paper deals with a general framework for inexact forward–backward algorithms aimed at minimizing the sum of an analytic function and a lower semicontinuous, subanalytic, convex term. Such framework relies on an implementable inexactness condition for the computation of the proximal operator, and a linesearch procedure which is possibly performed whenever a variable metric is … Read more
In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with … Read more
We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters … Read more
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, … Read more
We consider an integrated pricing and routing problem on a network. The problem is motivated by applications in freight transportation such as package delivery and less-than-truckload shipping services. The decision maker sets a price for each origin-destination pair of the network, which determines the demand flow that needs to be served. The flows are then … Read more
Naturally imbalanced freight flows force consolidation carriers to reposition resources empty. When constructing empty repositioning plans, the cost of repositioning resources empty needs to be weighed against the cost of corrective actions in case of unavailable resources. This is especially challenging given the uncertainty of future demand. We design and implement a robust rolling horizon … Read more
The aim of this study is to develop a solution to the problem of distribution of goods proposed by the Mathematical Competitive Game 2017-2018, jointly organized by the French Federation of Mathematical Games and Mathematical Modelling Company. Referred to as a production-inventory-distribution-routing problem (PIDRP), it is an NP-hard combinatorial optimization problem, which received the least … Read more
This paper proposes an optimization framework for retailers that are involved in demand response (DR) programs. In a first phase responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Then, the retailer exploits in a second phase this preliminary non-coordinated solution to implement a strategy … Read more
This paper proposes a two-phase optimization framework for users that are involved in demand response (DR) programs. In a first phase, responsive users optimize their own household consumption, characterizing not only their appliances and equipments but also their comfort preferences. Subsequently, the aggregator exploits in a second phase this preliminary non-coordinated solution by implementing a … Read more