We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower semicontinuous function on this product space is reached on the tensorial product of finite mixtures of extreme...
Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming methods. In contrast, deep learning o...
We consider a time-dependent shortest path problem with possible waiting at each node and a global bound W on the total waiting time. The goal is to minimize only the time traveled along the edges of the path, not including the waiting time. We prove that the problem can be solved in polynomial time when the travel time functions are piecewise line...
This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are analytically not tractable. The procedure applies to posterior probability densities that are continuously differen-t...
We introduce a new problem, which is an extension of the classical job shop with tooling constraints. We study it from 3 different aspects: scheduling, matrix visualization and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to prove several of its NP-Hard and polynomial subcases. T...
19 pages, 2 figures, new title, added references and discussions
In this paper we benchmark five variants of CMA-ES for optimization in large dimension on the novel large scale testbed of COCO under default or modified parameter settings. In particular, we compare the performance of the separable CMA-ES, of VD-CMA-ES and VkD-CMA-ES, of two implementations of the Limited Memory CMA-ES and of the Rank m Evolution ...
We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × n-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given p − 1 fixed solutions....
In this paper, we propose a comparative benchmark of MO-CMA-ES, COMO-CMA-ES (recently introduced in [12]) and NSGA-II, using the COCO framework for performance assessment and the Bi-objective test suite bbob-biobj. For a fixed number of points p, COMO-CMA-ES approximates an optimal p-distribution of the Hypervolume Indicator. While not designed to ...
