We consider least squares semidefinite programming (LSSDP) where the primal matrix variable must satisfy given linear equality and inequality constraints, and must also lie in the intersection of the cone of symmetric positive semidefinite matrices and a simple polyhedral set. We propose an inexact accelerated block coordinate descent (ABCD) method for solving LSSDP via its dual, which can be r...

We write explicit and self-contained asymptotic expressions for the tensorial B, C and D Passarino-Veltman functions. These include quadratic and linear logarithmic terms, as well as subleading constant terms. Only mass-suppressed O(m2/s) contributions are neglected. We discuss the usefulness of such expressions, particularly for studying oneloop effects in 2-to-2 body processes at high energy....

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic). We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem. We also develop a connection, fo...

The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac Kean-Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with quadratic cost; on the other hand, the propagation of chaos for particle systems in mean field in...

We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We provide explicit solutions for investors with exponential, logarithmic as well as power utility and show that they are unique if the constraints are convex. Our approach is based on martingale methods that rely on results on the existence and un...

Abstract In [Sa], it was proved that the Selberg zeta function for SL2(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL2(Z). As applications, we study the Brun-Titc...

A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of Õ(n) elementary gates in logarithmic depth. This is essentially a quadratic improvement in size (and in width times ...

State of the art statistical estimators for high-dimensional problems take the form of regularized, and hence non-smooth, convex programs. A key facet of these statistical estimation problems is that these are typically not strongly convex under a high-dimensional sampling regime when the Hessian matrix becomes rankdeficient. Under vanilla convexity however, proximal optimization methods attain...