相关论文: The Numerically Optimized Regulator and the Functi…

This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using Spectral Submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with…

We propose a renormalon-inspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge beta-function coefficients by the portion containing the highest power of…

As one of the key components of perturbative QCD theory, it is helpful to find a systematic and reliable way to set the renormalization scale for a high-energy process. The conventional treatment is to take a typical momentum as the…

In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered…

We introduce a dynamical lattice regulator for Euclidean quantum field theories on a fixed hypercubic graph $\Lambda\simeq\mathbb{Z}^d$, in which the embedding $x:\Lambda\to\mathbb{R}^d$ is promoted to a dynamical field and integrated over…

We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…

Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be…

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling…

In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main assumption being that the third derivative of the objective…

A closed-form analytical expression is derived for the limiting empirical squared singular value density of a spreading (signature) matrix corresponding to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA) with…

We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically,…

Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…

Quantum optimal control in the presence of decoherence is difficult, particularly when not all Hamiltonian parameters are known precisely, as in quantum sensing applications. In this context, maximizing the sensitivity of the system is the…

We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…

We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson's hierarchical…

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…

A recent extension of a variationally optimized perturbation, combined with renormalization group properties in a straightforward way, can provide approximations to nonperturbative quantities such as the chiral symmetry breaking order…