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Convex combination

About: Convex combination is a(n) research topic. Over the lifetime, 7856 publication(s) have been published within this topic receiving 201051 citation(s).

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Papers
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Journal ArticleDOI
TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.

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Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

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4,540 citations


Book
21 Oct 1993-
Abstract: IX. Inner Construction of the Subdifferential.- X. Conjugacy in Convex Analysis.- XI. Approximate Subdifferentials of Convex Functions.- XII. Abstract Duality for Practitioners.- XIII. Methods of ?-Descent.- XIV. Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods.- XV. Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods.- Bibliographical Comments.- References.

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2,979 citations


Book ChapterDOI
Michael C. Grant1, Stephen Boyd1Institutions (1)
Abstract: We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved, using interiorpoint methods for smooth or cone convex programs.

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2,653 citations


Journal ArticleDOI
Xu-Dong Liu1, Stanley Osher1, Tony F. Chan1Institutions (1)
TL;DR: A new version of ENO (essentially non-oscillatory) shock-capturing schemes which is called weighted ENO, where, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, a convex combination of all candidates is used.

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Abstract: In this paper we introduce a new version of ENO (essentially non-oscillatory) shock-capturing schemes which we call weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combination of all candidates to achieve the essentially non-oscillatory property, while additionally obtaining one order of improvement in accuracy. The resulting weighted ENO schemes are based on cell averages and a TVD Runge-Kutta time discretization. Preliminary encouraging numerical experiments are given.

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2,635 citations


Journal ArticleDOI
TL;DR: This method can be regarded as a generalization of the methods discussed in [1–4] and applied to the approximate solution of problems in linear and convex programming.

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Abstract: IN this paper we consider an iterative method of finding the common point of convex sets. This method can be regarded as a generalization of the methods discussed in [1–4]. Apart from problems which can be reduced to finding some point of the intersection of convex sets, the method considered can be applied to the approximate solution of problems in linear and convex programming.

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2,456 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20223
2021170
2020186
2019176
2018197
2017327

Top Attributes

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Topic's top 5 most impactful authors

Shouming Zhong

16 papers, 254 citations

Shumin Fei

14 papers, 265 citations

Jonathan M. Borwein

10 papers, 1.6K citations

Rolf Schneider

10 papers, 430 citations

Vaithilingam Jeyakumar

10 papers, 288 citations