We introduce and study the notion of a logarithmic vertex algebra, which is algebra with singularities in operator product expansion quantum fields; thus providing rigorous formulation algebraic properties fields conformal field theory. develop framework that allows many results about algebras to be extended algebras, including particular Borcherds identity Kac Existence Theorem. Several exampl...

We present a logarithmic barrier interior-point method for solving a second-order cone programming problem. Newton’s method is used to compute the descent direction, and majorant functions are used as an efficient alternative to line search methods to determine the displacement step along the direction. The efficiency of our method is shown by presenting numerical experiments.

We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in [BL00]. We prove by Prékopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on Rn. This inequality implies results proved by Bobkov and Ledoux, the Euclidean Logarithmic Sobolev inequality generalized in the last years and it also implies some convex...

We propose a strategy for building up the linear program while using a logarithmic barrier method. The method starts with a (small) subset of the dual constraints, and follows the corresponding central path until the iterate is close to (or violates) one of the constraints, which is in turn added to the current system. This process is repeated until an optimal solution is reached. If a constrai...

In this paper, we presented a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The method generates the new iterate by searching the optimal step size along the descent direction. Global convergence of the new method is proved under certain assumptions.

This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part II), we develop logarithmic formal calculus and study logarithmic intertwining operators. In this paper, Part II of a series of eight papers on logarithmic tensor category theory, we develop ...