相关论文: On Second Order Conditions in the Multivariate Blo…

The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…

Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). This extension is strict, i.e., higher-order processes equipped with parameterization is computationally…

The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this work, we study interpolation conditions for linear operators…

Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the…

This work presents the Second-Order Sensitivity Analysis Methodology (2nd-ASAM) for nonlinear systems. This methodology yields exactly and efficiently the second-order functional derivatives of system responses (associated with physical,…

We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…

Theoretical considerations predict a specific hierarchy among ratios of net-baryon number cumulants ($\chi_n$, where $n$ is the order of cumulant) in the vicinity of the transition from the low-temperature hadronic phase to the high…

Using a regularization with the properties of dimensional regularization, higher order local consistency conditions on one loop anomalies and divergent counterterms are given. They are derived without any a priori assumption on the form of…

In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor-Hood elements, under the assumption of the…

Two-stage superposition choice procedures, which sequentially apply two choice procedures so that the result of the first choice procedure is the input for the second choice procedure, are studied. We define which of them satisfy given…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous…

In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches…