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We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

Optimization and Control · Mathematics 2022-03-01 Yossi Arjevani , Yair Carmon , John C. Duchi , Dylan J. Foster , Nathan Srebro , Blake Woodworth

This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…

Optimization and Control · Mathematics 2024-12-12 Nguyen Thi Thu Huong

In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based…

Information Theory · Computer Science 2013-04-02 Lazar Velimirovic , Zoran Peric , Miomir Stankovic , Jelena Nikolic

Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…

Optimization and Control · Mathematics 2025-06-16 Andrea Cristofari

Tensor optimization is crucial to massive machine learning and signal processing tasks. In this paper, we consider tensor optimization with a convex and well-conditioned objective function and reformulate it into a nonconvex optimization…

Optimization and Control · Mathematics 2022-02-18 Shuang Li , Qiuwei Li

It is well-known that accelerated gradient first order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However,…

Optimization and Control · Mathematics 2024-07-02 Ilya Kuruzov , Fedor Stonyakin

The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations…

Optimization and Control · Mathematics 2021-10-12 Figen Oztoprak , Richard Byrd , Jorge Nocedal

In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what problem…

Optimization and Control · Mathematics 2021-03-08 Naoki Hamada , Shunsuke Ichiki

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

Machine Learning · Computer Science 2022-03-10 Marwa El Halabi , Stefanie Jegelka

We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give…

Computer Vision and Pattern Recognition · Computer Science 2022-06-22 Zhakshylyk Nurlanov , Daniel Cremers , Florian Bernard

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

Data Structures and Algorithms · Computer Science 2018-06-29 Amit Levi , Yuichi Yoshida

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

Computer Vision and Pattern Recognition · Computer Science 2020-10-22 Huu Le , Christopher Zach , Edward Rosten , Oliver J. Woodford

This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…

Optimization and Control · Mathematics 2025-02-03 Xiaojun Chen , Carl Kelley

Semantic segmentation is fundamental to vision systems requiring pixel-level scene understanding, yet deploying it on resource-constrained devices demands efficient architectures. Although existing methods achieve real-time inference…

Computer Vision and Pattern Recognition · Computer Science 2025-08-13 Shi-Chen Zhang , Yunheng Li , Yu-Huan Wu , Qibin Hou , Ming-Ming Cheng

In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving…

Information Theory · Computer Science 2013-11-22 Zoran H. Peric , Lazar Velimirovic , Miomir Stankovic , Aleksandra Jovanovic , Dragan Antic

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

Statistics Theory · Mathematics 2025-08-04 Jelena Bradic , Victor Chernozhukov , Whitney K. Newey , Yinchu Zhu

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…

Optimization and Control · Mathematics 2025-07-23 Casey Garner , Gilad Lerman , Shuzhong Zhang

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

Numerical Analysis · Mathematics 2024-06-21 Nicat Aliyev , Emre Mengi

Scalar curvature constraints can be studied by means of splitting procedures. The success of this strategy depends on the control we can get on its splitting factors. We introduce canonical so-called minimal splitting factors. They have…

Differential Geometry · Mathematics 2022-03-30 Joachim Lohkamp