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This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any…

Statistics Theory · Mathematics 2012-12-27 Arun Chandrasekhar , Victor Chernozhukov , Francesca Molinari , Paul Schrimpf

In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…

Optimization and Control · Mathematics 2024-04-10 Hoa T. Bui , Regina S. Burachik , Evgeni A. Nurminski , Matthew K. Tam

We consider the problem of finding the best harmonic or analytic approximant to a given function. We discuss when the best approximant is unique, and what regularity properties the best approximant inherits from the original function. All…

Functional Analysis · Mathematics 2007-05-23 Dmitry Khavinson , John E. McCarthy , Harold S. Shapiro

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

Numerical Analysis · Mathematics 2018-03-06 Michael Griebel , Peter Oswald

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…

Optimization and Control · Mathematics 2017-01-19 Jason Xu , Eric C. Chi , Meng Yang , Kenneth Lange

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Pierre Moulin

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…

Optimization and Control · Mathematics 2022-02-04 Gregory Dexter , Agniva Chowdhury , Haim Avron , Petros Drineas

We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…

Numerical Analysis · Mathematics 2017-03-01 Dinh Dũng , Charles A. Micchelli , Vu Nhat Huy

The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…

Functional Analysis · Mathematics 2018-02-28 Muhammad Aqeel Ahmad Khan , Hafiza Arham Maqbool

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…

Optimization and Control · Mathematics 2018-05-24 Xuefeng Bao , Zhi-Hong Mao , Nitin Sharma

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2022-09-26 Agniva Chowdhury , Gregory Dexter , Palma London , Haim Avron , Petros Drineas

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

Information Theory · Computer Science 2015-07-20 Zhenliang Zhang , Yuan Wang , Edwin K. P. Chong , Ali Pezeshki , Louis Scharf

Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…

Computational Geometry · Computer Science 2021-07-13 Jonathan Klawitter , Felix Klesen , Alexander Wolff

For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal…

Functional Analysis · Mathematics 2023-07-11 Christopher Felder

We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the…

Classical Analysis and ODEs · Mathematics 2019-08-15 Catherine Bénéteau , Matthew Fleeman , Dmitry Khavinson , Daniel Seco , Alan Sola

This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…

Functional Analysis · Mathematics 2018-03-07 Abdul Ghaffar , Zafar Ullah , Muhammad Aqeel Ahmad Khan , Faisal Mumtaz

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

Computer Vision and Pattern Recognition · Computer Science 2020-07-07 Wei Lian , WangMeng Zuo , Lei Zhang

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…

Optimization and Control · Mathematics 2020-09-14 Kimia Ghobadi , Houra Mahmoudzadeh

Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…

Computational Complexity · Computer Science 2026-05-12 Amey Bhangale , Yezhou Zhang

We consider ILPs, where each variable corresponds to an integral point within a polytope $\mathcal{P}$, i. e., ILPs of the form $\min\{c^{\top}x\mid \sum_{p\in\mathcal P\cap \mathbb Z^d} x_p p = b, x\in\mathbb Z^{|\mathcal P\cap \mathbb…

Computational Complexity · Computer Science 2020-10-20 Sebastian Berndt , Klaus Jansen , Alexandra Lassota