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Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
This paper is devoted to the study of operator-valued Hardy spaces via wavelet method. This approach is parallel to that in noncommutative martingale case. We show that our Hardy spaces defined by wavelet coincide with those introduced by…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection,…
When examined through the lens of their residual streams, a puzzling property emerges in transformer networks: residual contributions (e.g., attention heads) sometimes specialize in specific tasks or input attributes. In this paper, we…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry, from the theoretical, the algorithmic, and the practical point of view. In this paper, we present a…
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently…
Many graph embedding approaches have been proposed for knowledge graph completion via link prediction. Among those, translating embedding approaches enjoy the advantages of light-weight structure, high efficiency and great interpretability.…
We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the…
Detecting visual relationships, i.e. <Subject, Predicate, Object> triplets, is a challenging Scene Understanding task approached in the past via linguistic priors or spatial information in a single feature branch. We introduce a new deeply…
The Rotary Position Embedding (RoPE) mechanism has become a powerful enhancement to the Transformer architecture, which enables models to capture token relationships when encoding positional information. However, the RoPE mechanisms make…
A construction of integrable hamiltonian systems associated with different graded realizations of untwisted loop algebras is proposed. Such systems have the form of Euler - Arnold equations on orbits of loop algebras. The proof of…
Saddle point problems arise in a variety of applications, e.g., when solving the Stokes equations. They can be formulated such that the system matrix is symmetric, but indefinite, so the variational convergence theory that is usually used…
The $\mathcal{VU}$-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain $\mathcal{V}$-space and its orthogonal $\U$-space, such that the…
This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…
This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of…
We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex…
Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…