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We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…
We study the equivariant cobordism rings for the action of a torus $T$ on smooth varieties over an algebraically closed field of characteristic zero. We prove a theorem describing the rational $T$-equivariant cobordism rings of smooth…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is…
We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes including the optimal solution selection problem and the optimal Nash equilibrium (NE)…
Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of…
We use vector bundles to study the locus of totally mixed Nash equilibria of an $n$-player game in normal form, which we call the Nash equilibrium scheme. When the payoff tensor format is balanced, we study the Nash discriminant variety,…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
We prove that the evolutionary Navier-Stokes equation in n-D torus with initial data in the class of distributions has an unique solution (local in t) that is analytic by all variables. This solution presents as a series globally.
We define the equivariant Cox ring of a normal variety with algebraic group action. We study algebraic and geometric aspects of this object and show how it is related to the ordinary Cox ring. Then, we specialize to the case of normal…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach…
In this paper, we study the rationality problem for multinorm one tori, a natural generalization of norm one tori. For multinorm one tori that split over finite Galois extensions with nilpotent Galois group, we prove that stable rationality…
We give a description of the equisingularity of a family of normal surface singularities by numerical invariants belonging to them. By equisingularity we mean Whitney regularity or a more restrictive condition using the Nash modification.
Conformal supergravity provides an effective off-shell formalism to study higher derivative actions. We show that the $D=4$, $\mathcal{N}=2$ theory admits equivariantly closed forms. These may be used to compute closed-form expressions for…
We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs, the KKT sets can be represented as unions of simpler sets…
We introduce conditions on cones of normal toric varieties under which the polyhedron defining the normalized Nash blowup does not depend on the characteristic of the base field. As a consequence, we deduce several results on the resolution…
This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for…
In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient…