We study the fundamental problem of computing an arbitrary Nash equilibrium in bimatrix games. We start by proposing a novel characterization of the set of Nash equilibria, via a bijective map to the solution set of a (parameterized) quadratic program, whose feasible space is the (highly structured) set of correlated equilibria. We then proceed by proposing new subclasses of bimatrix games for ...

We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the socalled Hardy-Littlewood majorant property. We derive this from a rather more general result which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a r...

We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton’s method under Lipschitz conditions we show that the famous Newton–Kantorovich hypo...

We provide a local convergence analysis of inexact Newton–like methods in a Banach space setting under flexible majorant conditions. By introducing center–Lipschitz–type condition, we provide (under the same computational cost) a convergence analysis with the following advantages over earlier work [9]: finer error bounds on the distances involved, and a larger radius of convergence. Special cas...

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regular-ized least squares estimator enjoys a nonasymptotic property,...

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares estimator enjoys a nonasymptotic property, ...

In this article, we study the multiplicity of solutions for a class fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under appropriate assumption, prove that there are at least two equation by Nehari manifold Ekeland variational principle, one which is ground state solution.

In the article, existence of solutions for Van der Pol differential equation is proved, and approximate structure such in analyticity domain obtained. proof, majorant method was applied not to right side equation, as per usual, but solution nonlinear under consideration. Results numerical study are presented.

Computational fluid dynamics (CFD) is a powerful numerical tool that is becoming widely used to simulate many processes in the industry. In this work study of the stirred tank with 7 types of concave blade with CFD was presented. In the modeling of the impeller rotation, sliding mesh (SM) technique was used and RNG-k-ε model was selected for turbulence. Power consumption in various speeds in th...