Fixed Point Theory and Applications最新文献_第3页

Unsteady non-Newtonian fluid flow with heat transfer and Tresca’s friction boundary conditions 非定常非牛顿流体传热与Tresca摩擦边界条件

Fixed Point Theory and Applications Pub Date : 2022-01-24 DOI: 10.1186/s13663-022-00714-x

Paoli, Laetitia

引用次数: 0

Numerical analysis of doubly-history dependent variational inequalities in contact mechanics 接触力学中双历史相关变分不等式的数值分析

Fixed Point Theory and Applications Pub Date : 2021-12-13 DOI: 10.1186/s13663-021-00710-7

Xu, Wei, Wang, Cheng, He, Mingyan, Chen, Wenbin, Han, Weimin, Huang, Ziping

引用次数: 3

Market equilibria and money 市场均衡和货币

Fixed Point Theory and Applications Pub Date : 2021-11-15 DOI: 10.1186/s13663-021-00705-4

Flåm, Sjur Didrik

引用次数: 2

Asymptotic behavior of Newton-like inertial dynamics involving the sum of potential and nonpotential terms 涉及势项和非势项和的类牛顿惯性动力学的渐近行为

Fixed Point Theory and Applications Pub Date : 2021-10-18 DOI: 10.1186/s13663-021-00702-7

Adly, Samir, Attouch, Hedy, Vo, Van Nam

{"title":"Asymptotic behavior of Newton-like inertial dynamics involving the sum of potential and nonpotential terms","authors":"Adly, Samir, Attouch, Hedy, Vo, Van Nam","doi":"10.1186/s13663-021-00702-7","DOIUrl":"https://doi.org/10.1186/s13663-021-00702-7","url":null,"abstract":"In a Hilbert space $mathcal{H}$ , we study a dynamic inertial Newton method which aims to solve additively structured monotone equations involving the sum of potential and nonpotential terms. Precisely, we are looking for the zeros of an operator $A= nabla f +B $ , where ∇f is the gradient of a continuously differentiable convex function f and B is a nonpotential monotone and cocoercive operator. Besides a viscous friction term, the dynamic involves geometric damping terms which are controlled respectively by the Hessian of the potential f and by a Newton-type correction term attached to B. Based on a fixed point argument, we show the well-posedness of the Cauchy problem. Then we show the weak convergence as $tto +infty $ of the generated trajectories towards the zeros of $nabla f +B$ . The convergence analysis is based on the appropriate setting of the viscous and geometric damping parameters. The introduction of these geometric dampings makes it possible to control and attenuate the known oscillations for the viscous damping of inertial methods. Rewriting the second-order evolution equation as a first-order dynamical system enables us to extend the convergence analysis to nonsmooth convex potentials. These results open the door to the design of new first-order accelerated algorithms in optimization taking into account the specific properties of potential and nonpotential terms. The proofs and techniques are original and differ from the classical ones due to the presence of the nonpotential term.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator 两个广义单调算子和一个正则算子和的自适应分割算法

Fixed Point Theory and Applications Pub Date : 2021-10-04 DOI: 10.1186/s13663-021-00701-8

Dao, Minh N., Phan, Hung M.

引用次数: 3

A generalized multivariable Newton method 广义多变量牛顿法

Fixed Point Theory and Applications Pub Date : 2021-09-20 DOI: 10.1186/s13663-021-00700-9

Burachik, Regina S., Caldwell, Bethany I., Kaya, C. Yalçın

引用次数: 1

Strongly regular points of mappings 映射的强正则点

Fixed Point Theory and Applications Pub Date : 2021-09-06 DOI: 10.1186/s13663-021-00699-z

Abbasi, Malek, Théra, Michel

引用次数: 4

Convergence of proximal splitting algorithms in (operatorname{CAT}(kappa)) spaces and beyond 近端分裂算法在(operatorname{CAT}(kappa))空间及以后的收敛性

Fixed Point Theory and Applications Pub Date : 2021-08-24 DOI: 10.1186/s13663-021-00698-0

Lauster, Florian, Luke, D. Russell

引用次数: 1

Learning without loss 无损失的学习

Fixed Point Theory and Applications Pub Date : 2021-07-26 DOI: 10.1186/s13663-021-00697-1

Veit Elser

{"title":"Learning without loss","authors":"Veit Elser","doi":"10.1186/s13663-021-00697-1","DOIUrl":"https://doi.org/10.1186/s13663-021-00697-1","url":null,"abstract":"We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed–reflect–reflect (RRR), derives its steps from projections to local constraints. In neural networks one such projection makes the minimal modification to the inputs x, the associated weights w, and the pre-activation value y at each neuron, to satisfy the equation $xcdot w=y$ . These projections, along with a host of other local projections (constraining pre- and post-activations, etc.) can be partitioned into two sets such that all the projections in each set can be applied concurrently—across the network and across all data in the training batch. This partitioning into two sets is analogous to the situation in phase retrieval and the setting for which the general purpose RRR optimizer was designed. Owing to the novelty of the method, this paper also serves as a self-contained tutorial. Starting with a single-layer network that performs nonnegative matrix factorization, and concluding with a generative model comprising an autoencoder and classifier, all applications and their implementations by projections are described in complete detail. Although the new approach has the potential to extend the scope of neural networks (e.g. by defining activation not through functions but constraint sets), most of the featured models are standard to allow comparison with stochastic gradient descent.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces 希尔伯特空间中哈默斯坦积分结论近似解的惯性型算法

Fixed Point Theory and Applications Pub Date : 2021-03-29 DOI: 10.1186/s13663-021-00691-7

A. U. Bello, M. T. Omojola, J. Yahaya

引用次数: 0