Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Approximation algorithm. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

User’s guide to viscosity solutions of second order partial differential equations

Abstract: The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions

Convex analysis and variational problems

Abstract: Preface to the classics edition Preface Part I. Fundamentals of Convex Analysis. I. Convex functions 2. Minimization of convex functions and variational inequalities 3. Duality in convex optimization Part II. Duality and Convex Variational Problems. 4. Applications of duality to the calculus of variations (I) 5. Applications of duality to the calculus of variations (II) 6. Duality by the minimax theorem 7. Other applications of duality Part III. Relaxation and Non-Convex Variational Problems. 8. Existence of solutions for variational problems 9. Relaxation of non-convex variational problems (I) 10. Relaxation of non-convex variational problems (II) Appendix I. An a priori estimate in non-convex programming Appendix II. Non-convex optimization problems depending on a parameter Comments Bibliography Index.

End-to-End Object Detection with Transformers

Abstract: We present a new method that views object detection as a direct set prediction problem. Our approach streamlines the detection pipeline, effectively removing the need for many hand-designed components like a non-maximum suppression procedure or anchor generation that explicitly encode our prior knowledge about the task. The main ingredients of the new framework, called DEtection TRansformer or DETR, are a set-based global loss that forces unique predictions via bipartite matching, and a transformer encoder-decoder architecture. Given a fixed small set of learned object queries, DETR reasons about the relations of the objects and the global image context to directly output the final set of predictions in parallel. The new model is conceptually simple and does not require a specialized library, unlike many other modern detectors. DETR demonstrates accuracy and run-time performance on par with the well-established and highly-optimized Faster RCNN baseline on the challenging COCO object detection dataset. Moreover, DETR can be easily generalized to produce panoptic segmentation in a unified manner. We show that it significantly outperforms competitive baselines. Training code and pretrained models are available at this https URL.

Nonlinear scalar field equations, I existence of a ground state

Abstract: 1. The Main Result; Examples . . . . . . . . . . . . . . . . . . . . . . . 316 2. Necessary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 319 3. The Constrained Minimization Method . . . . . . . . . . . . . . . . . . 323 4. Further Properties of the Solution . . . . . . . . . . . . . . . . . . . . 328 5. The \"Zero Mass\" Case . . . . . . . . . . . . . . . . . . . . . . . . . 332 6. The Case of Dimension N = 1 (Necessary and Sufficient Conditions) . . . . . 335 Appendix. Technical Results . . . . . . . . . . . . . . . . . . . . . . . . 338

Mean Field Games

Abstract: We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects...). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited information (or visibility) on the “game”. Each player chooses his optimal strategy in view of the global (or macroscopic) informations that are available to him and that result from the actions of all players. In the three examples we mention here, we derive a mean-field problem which consists in nonlinear differential equations. These equations are of a new type and our main goal here is to study them and establish their links with various fields of Analysis. We show in particular that these nonlinear problems are essentially well-posed problems i.e., have unique solutions. In addition, we give various limiting cases, examples and possible extensions. And we mention many open problems.