Journal of Nonsmooth Analysis and Optimization最新文献_第2页

Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications Abs-Normal nlp与mpcc的关系第1部分:强约束条件

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-07-29 DOI: 10.46298/jnsao-2021-6672

L. C. Hegerhorst-Schultchen, C. Kirches, M. Steinbach

引用次数: 1

Asymptotic stationarity and regularity for nonsmooth optimization problems 非光滑优化问题的渐近平稳性和正则性

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-06-17 DOI: 10.46298/jnsao-2020-6575

P. Mehlitz

引用次数: 21

Inexact and Stochastic Generalized Conditional Gradient with Augmented Lagrangian and Proximal Step 具有增广拉格朗日和近步的非精确随机广义条件梯度

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-05-11 DOI: 10.46298/jnsao-2021-6480

Antonio Silveti-Falls, C. Molinari, J. Fadili

{"title":"Inexact and Stochastic Generalized Conditional Gradient with Augmented Lagrangian and Proximal Step","authors":"Antonio Silveti-Falls, C. Molinari, J. Fadili","doi":"10.46298/jnsao-2021-6480","DOIUrl":"https://doi.org/10.46298/jnsao-2021-6480","url":null,"abstract":"In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in [25], which we denote ICGALP , that allow for errors in the computation of several important quantities. In particular this allows one to compute some gradients, proximal terms, and/or linear minimization oracles in an inexact fashion that facilitates the practical application of the algorithm to computationally intensive settings, e.g., in high (or possibly infinite) dimensional Hilbert spaces commonly found in machine learning problems. The algorithm is able to solve composite minimization problems involving the sum of three convex proper lower-semicontinuous functions subject to an affine constraint of the form Ax = b for some bounded linear operator A. Only one of the functions in the objective is assumed to be differentiable, the other two are assumed to have an accessible proximal operator and a linear minimization oracle. As main results, we show convergence of the Lagrangian values (so-called convergence in the Bregman sense) and asymptotic feasibility of the affine constraint as well as strong convergence of the sequence of dual variables to a solution of the dual problem, in an almost sure sense. Almost sure convergence rates are given for the Lagrangian values and the feasibility gap for the ergodic primal variables. Rates in expectation are given for the Lagrangian values and the feasibility gap subsequentially in the pointwise sense. Numerical experiments verifying the predicted rates of convergence are shown as well.","PeriodicalId":250939,"journal":{"name":"Journal of Nonsmooth Analysis and Optimization","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115873581","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

Constructing a subgradient from directional derivatives for functions of two variables 从两个变量函数的方向导数构造子梯度

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-01-29 DOI: 10.46298/jnsao-2020-6061

Kamil A. Khan, Yingwei Yuan

{"title":"Constructing a subgradient from directional derivatives for functions of two variables","authors":"Kamil A. Khan, Yingwei Yuan","doi":"10.46298/jnsao-2020-6061","DOIUrl":"https://doi.org/10.46298/jnsao-2020-6061","url":null,"abstract":"For any scalar-valued bivariate function that is locally Lipschitz continuous and directionally differentiable, it is shown that a subgradient may always be constructed from the function's directional derivatives in the four compass directions, arranged in a so-called \"compass difference\". When the original function is nonconvex, the obtained subgradient is an element of Clarke's generalized gradient, but the result appears to be novel even for convex functions. The function is not required to be represented in any particular form, and no further assumptions are required, though the result is strengthened when the function is additionally L-smooth in the sense of Nesterov. For certain optimal-value functions and certain parametric solutions of differential equation systems, these new results appear to provide the only known way to compute a subgradient. These results also imply that centered finite differences will converge to a subgradient for bivariate nonsmooth functions. As a dual result, we find that any compact convex set in two dimensions contains the midpoint of its interval hull. Examples are included for illustration, and it is demonstrated that these results do not extend directly to functions of more than two variables or sets in higher dimensions.","PeriodicalId":250939,"journal":{"name":"Journal of Nonsmooth Analysis and Optimization","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125229335","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: 1

Uniform Regularity of Set-Valued Mappings and Stability of Implicit Multifunctions 集值映射的一致正则性与隐多函数的稳定性

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-01-15 DOI: 10.46298/jnsao-2021-6599

N. D. Cuong, A. Kruger

引用次数: 3

First-order differentiability properties of a class of equality constrained optimal value functions with applications 一类等式约束的最优值函数的一阶可微性及其应用

Journal of Nonsmooth Analysis and Optimization Pub Date : 2020-01-13 DOI: 10.46298/jnsao-2020-6034

K. Sturm

引用次数: 1

Optimal Control of an abstract Evolution Variational Inequality with Application in Homogenized Plasticity 一类抽象演化变分不等式的最优控制及其在均匀塑性中的应用

Journal of Nonsmooth Analysis and Optimization Pub Date : 2019-09-30 DOI: 10.46298/jnsao-2020-5800

H. Meinlschmidt, C. Meyer, S. Walther

引用次数: 5