Open J. Math. Optim.最新文献

Inertial-relaxed splitting for composite monotone inclusions 复合单调包体的惯性松弛分裂

Open J. Math. Optim. Pub Date : 2023-02-02 DOI: 10.5802/ojmo.22

Ernesto Oré, P. Mahey, Eladio Ocan͂a

引用次数: 0

Short Paper - A note on the Frank-Wolfe algorithm for a class of nonconvex and nonsmooth optimization problems 关于一类非凸非光滑优化问题的Frank-Wolfe算法的注释

Open J. Math. Optim. Pub Date : 2023-01-24 DOI: 10.5802/ojmo.21

W. Oliveira

引用次数: 3

AC Optimal Power Flow: a Conic Programming relaxation and an iterative MILP scheme for Global Optimization 交流最优潮流:一个全局优化的二次规划松弛和迭代MILP方案

Open J. Math. Optim. Pub Date : 2022-11-02 DOI: 10.5802/ojmo.17

Antoine Oustry

引用次数: 1

Efficient optimization of the Held-Karp lower bound Held-Karp下界的有效优化

Open J. Math. Optim. Pub Date : 2021-11-03 DOI: 10.5802/ojmo.11

G. Righini

引用次数: 0

Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems 凸不等式约束系统误差界稳定性的刻画

Open J. Math. Optim. Pub Date : 2021-10-22 DOI: 10.5802/ojmo.13

Zhou Wei, M. Théra, J. Yao

{"title":"Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems","authors":"Zhou Wei, M. Théra, J. Yao","doi":"10.5802/ojmo.13","DOIUrl":"https://doi.org/10.5802/ojmo.13","url":null,"abstract":"In this paper, we mainly study error bounds for a single convex inequality and semi-infinite convex constraint systems, and give characterizations of stability of error bounds via directional derivatives. For a single convex inequality, it is proved that the stability of local error bounds under small perturbations is essentially equivalent to the non-zero minimun of the directional derivative at a reference point over the sphere, and the stability of global error bounds is proved to be equivalent to the strictly positive infimum of the directional derivatives, at all points in the boundary of the solution set, over the sphere as well as some mild constraint qualification. When these results are applied to semi-infinite convex constraint systems, characterizations of stability of local and global error bounds under small perturbations are also provided. In particular such stability of error bounds is proved to only require that all component functions in semi-infinite convex constraint systems have the same linear perturbation. Our work demonstrates that verifying the stability of error bounds for convex inequality constraint systems is, to some degree, equivalent to solving the convex optimization/minimization problems (defined by directional derivatives) over the sphere.","PeriodicalId":186223,"journal":{"name":"Open J. Math. Optim.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129221545","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: 2

Tight computationally efficient approximation of matrix norms with applications 矩阵规范的计算效率逼近及其应用

Open J. Math. Optim. Pub Date : 2021-10-08 DOI: 10.5802/ojmo.19

A. Juditsky, Georgios Kotsalis, A. Nemirovski

{"title":"Tight computationally efficient approximation of matrix norms with applications","authors":"A. Juditsky, Georgios Kotsalis, A. Nemirovski","doi":"10.5802/ojmo.19","DOIUrl":"https://doi.org/10.5802/ojmo.19","url":null,"abstract":"We address the problems of computing operator norms of matrices induced by given norms on the argument and the image space. It is known that aside of a fistful of\"solvable cases,\"most notably, the case when both given norms are Euclidean, computing operator norm of a matrix is NP-hard. We specify rather general families of norms on the argument and the images space (\"ellitopic\"and\"co-ellitopic,\"respectively) allowing for reasonably tight computationally efficient upper-bounding of the associated operator norms. We extend these results to bounding\"robust operator norm of uncertain matrix with box uncertainty,\"that is, the maximum of operator norms of matrices representable as a linear combination, with coefficients of magnitude $leq1$, of a collection of given matrices. Finally, we consider some applications of norm bounding, in particular, (1) computationally efficient synthesis of affine non-anticipative finite-horizon control of discrete time linear dynamical systems under bounds on the peak-to-peak gains, (2) signal recovery with uncertainties in sensing matrix, and (3) identification of parameters of time invariant discrete time linear dynamical systems via noisy observations of states and inputs on a given time horizon, in the case of\"uncertain-but-bounded\"noise varying in a box.","PeriodicalId":186223,"journal":{"name":"Open J. Math. Optim.","volume":"417 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123429392","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: 2

Estimating Shape Parameters of Piecewise Linear-Quadratic Problems 分段线性二次问题的形状参数估计

Open J. Math. Optim. Pub Date : 2021-09-23 DOI: 10.5802/ojmo.10

P. Zheng, K. Ramamurthy, A. Aravkin

{"title":"Estimating Shape Parameters of Piecewise Linear-Quadratic Problems","authors":"P. Zheng, K. Ramamurthy, A. Aravkin","doi":"10.5802/ojmo.10","DOIUrl":"https://doi.org/10.5802/ojmo.10","url":null,"abstract":"Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of penalty and its shape parameters, such as degree of asymmetry for the quantile loss, and transition point between linear and quadratic pieces for the Huber function. In this paper, we develop a statistical framework that can help the modeler to automatically tune shape parameters once the shape of the penalty has been chosen. The choice of the parameter is informed by the basic notion that each PLQ penalty should correspond to a true statistical density. The normalization constant inherent in this requirement helps to inform the optimization over shape parameters, giving a joint optimization problem over these as well as primary parameters of interest. A second contribution is to consider optimization methods for these joint problems. We show that basic ﬁrst-order methods can be immediately brought to bear, and design specialized extensions of interior point (IP) methods for PLQ problems that can quickly and eﬃciently solve the joint problem. Synthetic problems and larger-scale practical examples illustrate the utility of the approach. Code for the new IP method is implemented using the Julia language ( https://github.com/UW-AMO/shape-parameters/tree/ojmo ). Digital Object Identiﬁer 10.5802/ojmo.10 Acknowledgments The authors acknowledge the Washington Research Foundation Data Science Professorship.","PeriodicalId":186223,"journal":{"name":"Open J. Math. Optim.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122356462","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: 0

Gradient formulae for probability functions depending on a heterogenous family of constraints 基于异质约束的概率函数的梯度公式

Open J. Math. Optim. Pub Date : 2021-08-24 DOI: 10.5802/ojmo.9

W. Ackooij, P. Pérez-Aros

引用次数: 7

A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives 关于具有绝对和相对误差的近似加速向前-向后方法的说明，并且可能有强凸目标

Open J. Math. Optim. Pub Date : 2021-06-29 DOI: 10.5802/ojmo.12

Mathieu Barr'e, Adrien B. Taylor, F. Bach

引用次数: 5

Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measures 测度空间中凸优化的梯度方法的收敛速度

Open J. Math. Optim. Pub Date : 2021-05-18 DOI: 10.5802/ojmo.20

Lénaïc Chizat

引用次数: 19