English
Related papers

Related papers: Regularized HPE-type methods for solving monotone …

200 papers

We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…

Numerical Analysis · Mathematics 2020-12-30 Silvia Gazzola , Misha E. Kilmer , James G. Nagy , Oguz Semerici , Eric L. Miller

The extragradient (EG), introduced by G. M. Korpelevich in 1976, is a well-known method to approximate solutions of saddle-point problems and their extensions such as variational inequalities and monotone inclusions. Over the years,…

Optimization and Control · Mathematics 2023-03-31 Quoc Tran-Dinh

The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…

Mathematical Physics · Physics 2010-01-05 S. Yngve , B. Thidé

We present an algorithm for $hp$-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve-estimate-mark-refine paradigm. The solve phase…

Numerical Analysis · Mathematics 2023-01-25 Mitja Jančič , Gregor Kosec

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…

Numerical Analysis · Mathematics 2015-09-15 Patrick Henning , Mario Ohlberger , Barbara Verfürth

Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer…

Robotics · Computer Science 2025-08-21 Jiming Ren , Xuan Lin , Roman Mineyev , Karen M. Feigh , Samuel Coogan , Ye Zhao

This article considers the extension of two-grid $hp$-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when…

Numerical Analysis · Mathematics 2021-12-10 Scott Congreve , Paul Houston

We study logit-based multi-purchase choice models and develop an exact solution methodology for the resulting assortment optimization problems, which we show are NP-hard to approximate. We introduce a hypergraph representation that captures…

Optimization and Control · Mathematics 2026-03-30 Taotao He , Zhongqi Wu , Yating Zhang

We present both $hp$-a priori and $hp$-a posteriori error analysis of a mixed-order hybrid high-order (HHO) method to approximate second-order elliptic problems on simplicial meshes. Our main result on the $hp$-a priori error analysis is a…

Numerical Analysis · Mathematics 2025-07-25 Zhaonan Dong , Alexandre Ern

In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…

Optimization and Control · Mathematics 2020-10-06 Masaru Ito , Mituhiro Fukuda

Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…

Numerical Analysis · Mathematics 2026-02-17 Eric T. Chung , Hyea Hyun Kim , Xiang Zhong

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…

Numerical Analysis · Mathematics 2023-06-13 Wei-Fan Hu , Te-Sheng Lin , Yu-Hau Tseng , Ming-Chih Lai

This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…

Numerical Analysis · Mathematics 2021-08-23 Julianne Chung , Silvia Gazzola

We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…

Optimization and Control · Mathematics 2016-08-16 Maïtine Bergounioux , Mounir Haddou

In this paper, we consider the $\ell_0$ minimization problem whose objective function is the sum of $\ell_0$-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton…

Optimization and Control · Mathematics 2021-08-10 Xue Zhang , Xiaoqun Zhang

This paper presents a proximal bundle (PB) framework based on a generic bundle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging…

Optimization and Control · Mathematics 2023-03-29 Jiaming Liang , Renato D. C. Monteiro

We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the…

Probability · Mathematics 2024-09-04 Yvain Bruned , Pablo Linares

We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…

Optimization and Control · Mathematics 2026-02-06 Kevin Kurian Thomas Vaidyan , Michael P. Friedlander , Ahmet Alacaoglu

In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…

Analysis of PDEs · Mathematics 2014-01-03 Paul Cazeaux , Olivier Zahm

Finding optimal join orders is among the most crucial steps to be performed by query optimisers. Though extensively studied in data management research, the problem remains far from solved: While query optimisers rely on exhaustive search…

Databases · Computer Science 2025-10-24 Manuel Schönberger , Immanuel Trummer , Wolfgang Mauerer