相关论文: F-maximization along the RG flows: a proposal

We explore new IR phenomena and dualities, arising for product groups, in the context of N=1 supersymmetric gauge theories. The RG running of the multiple couplings can radically affect each other. For example, an otherwise IR interacting…

In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…

We study five-dimensional ${\cal N}=1$ Superconformal Field Theories of the linear quiver type. These are deformed by a relevant operator, corresponding to a homogeneous mass term for certain matter fields. The free energy is calculated at…

A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…

The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g.…

Nonequilibrium, ``fast switching'' estimates of equilibrium free energy differences, Delta F, are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced…

In this paper, a kind of non regular constraints and a principle for seeking critical point under the constraint are presented, where no Lagrange multiplier is involved. Let $E, F$ be two Banach spaces, $g: E\rightarrow F$ a $c^1$ map…

Solutions to nonlinear, nonconvex optimization problems can fail to satisfy the KKT optimality conditions even when they are optimal. This is due to the fact that unless constraint qualifications (CQ) are satisfied, Lagrange multipliers may…

In electricity networks with high penetration levels of renewable resources, Flexible Ramping Products (FRPs) are among the utilized measures for dealing with the potential fluctuations in the net demand. This paper investigates the impacts…

We study tightness properties of a Lagrangian dual (LD) bound for the nonconvex alternating current optimal power flow (ACOPF) problem. We show an LD bound that can be computed in a parallel, decentralized manner. Specifically, the proposed…

The main objective of this work is to study the existence of Lagrange multipliers for infinite dimensional problems under G\^ateux differentiability assumptions on the data. Our investigation follows two main steps: the proof of the…

This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…

In this work we provide a first order sensitivity analysis of some parameterized stochastic optimal control problems. The parameters can be given by random processes. The main tool is the one-to-one correspondence between the adjoint states…

A continuous sequence of infinitesimal unitary transformations, combined with an operator product expansion for vertex operators, is used to diagonalize the quantum sine-Gordon model for 2 pi < beta^2 < infinity. The leading order of this…

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a…

The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We…

Based on a characterization of the optimality of a feasible solution of a convex entropy minimization problem, one shows that the feasible solutions obtained using formally the Lagrange multipliers method are optimal.

Inspired by the Clebsch optimal control problem, we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraints related to a gauge symmetry. Its special feature is that…