Luis Nunes Vicente In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the … Read more
In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the … Read more
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with the non-differentiability of the outer function, we approximate the original non-smooth function using smoothing functions, which are continuously differentiable and approach … Read more
With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and … Read more
When dealing with a multi-objective optimization problem, obtaining a comprehensive representation of the Pareto front can be computationally expensive. Furthermore, identifying the most representative Pareto solutions can be difficult and sometimes ambiguous. A popular selection are the so-called Pareto knee solutions, where a small improvement in any objective leads to a large deterioration in at … Read more
We are interested in assessing the use of neural networks as surrogate models to approximate and minimize objective functions in optimization problems. While neural networks are widely used for machine learning tasks such as classification and regression, their application in solving optimization problems has been limited. Our study begins by determining the best activation function … Read more
Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates. One may also design algorithmic strategies that perform space exploration and seek improvement over the current point. The first type of strategy often provides … Read more
In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective … Read more
Managing all the mobility and transportation services with autonomous vehicles for users of a smart city requires determining the assignment of the vehicles to the users and their routing in conjunction with their speed. Such decisions must ensure low emission, efficiency, and high service quality by also considering the impact on traffic congestion caused by … Read more
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating … Read more