Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Autor: Josheski Dushko, Karamazova Elena, Apostolov Mico

Publikováno v: Applied Mathematics and Nonlinear Sciences, Vol 4, Iss 2, Pp 331-350 (2019)

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical d

Externí odkaz: https://doaj.org/article/07297c195777437ca109399dab19ed0a

Edgeworth's Conjecture with Infinitely many Commodities: L^1

Autor: Anderson, Robert M., Zame, William R.

Publikováno v: Econometrica, 1997 Mar 01. 65(2), 225-273.

Externí odkaz: https://www.jstor.org/stable/2171893

Stable Bounds on the Duality Gap of Separable Nonconvex Optimization Problems

Autor: Thomas Kerdreux, Igor Colin, Alexandre d’Aspremont

Publikováno v: Mathematics of Operations Research
Mathematics of Operations Research, 2022, ⟨10.1287/moor.2022.1291⟩

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland show that this produces an a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76b981e20614a0aab5297697b355e808
https://hal.science/hal-03837876

Approximation Bounds for Sparse Programs

Autor: Armin Askari, Alexandre d'Aspremont, Laurent El Ghaoui

Publikováno v: SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science, 2022, 4 (2), pp.514-530. ⟨10.1137/21M1398677⟩

International audience; We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bcf60cf0c3b18a480423b961f67a8a99

Tropical cellular automata : why urban fires propagate according to polyhedral balls

Autor: Gaubert, Stephane, Jones, Daniel

Publikováno v: AUTOMATA 2018-Cellular Automata and Discrete Complex Systems, 24th IFIP WG 1.5 International Workshop
AUTOMATA 2018-Cellular Automata and Discrete Complex Systems, 24th IFIP WG 1.5 International Workshop, Jun 2018, Ghent, Belgium

International audience; In order to analyse the propagation of fire in urban areas, we study a deterministic percolation model on a regular grid in which fire propagates from a point to a bounded neighbourhood of this point, with time constants depen

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::8cb270c6c01a238e409e95bce0166745
https://hal.inria.fr/hal-01967561/document