Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes

2004 ◽  
pp. 327-352 ◽  
Author(s):  
C. A. Meyer ◽  
C. A. Floudas
Keyword(s):  
Concave Envelopes

scholarly journals On the Jensen convex and Jensen concave envelopes of means

2020 ◽  
Author(s):  
Zsolt Páles ◽  
Paweł Pasteczka
Keyword(s):  
Quasiarithmetic Means ◽  
Concave Envelopes

Abstract In recent papers, the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper concave quasiarithmetic envelope.

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes

2004 ◽  
Vol 29 (2) ◽  
pp. 125-155 ◽  
Author(s):  
Clifford A. Meyer ◽  
Christodoulos A. Floudas
Keyword(s):  
Concave Envelopes

Explicit convex and concave envelopes through polyhedral subdivisions

2012 ◽  
Vol 138 (1-2) ◽  
pp. 531-577 ◽  
Author(s):  
Mohit Tawarmalani ◽  
Jean-Philippe P. Richard ◽  
Chuanhui Xiong
Keyword(s):  
Concave Envelopes

Dynamics in the fundamental solution of a non-convex conservation law

2015 ◽  
Vol 146 (1) ◽  
pp. 169-193
Author(s):  
Yong-Jung Kim ◽  
Young-Ran Lee
Keyword(s):  
Fundamental Solution ◽  
Conservation Law ◽  
Global Dynamics ◽  
Flux Function ◽  
Convexity Assumption ◽  
Inflection Points ◽  
Scalar Conservation Law ◽  
Comprehensive Picture ◽  
Scalar Conservation ◽  
Concave Envelopes

There is a huge jump in the theory of conservation laws if the convexity assumption is dropped. We study a scalar conservation law without the convexity assumption by monitoring the dynamics in the fundamental solution. We introduce three shock types in addition to the usual genuine shock: left-, right- and double-sided contacts. There are three kinds of phenomenon for these shocks, called branching, merging and transforming. All of these shocks and phenomena can be observed if the flux function has two inflection points. A comprehensive picture of a global dynamics of a non-convex flux is discussed in terms of characteristic maps and dynamical convex–concave envelopes.

scholarly journals A Boundary Construction Algorithm for a Complex Planar Point Set

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhenxiu Liao ◽  
Guodong Shi
Keyword(s):  
Delaunay Triangulation ◽  
State Of The Art ◽  
Rough Boundary ◽  
Boundary Extraction ◽  
Point Density ◽  
Local Areas ◽  
Point Set ◽  
Boundary Construction ◽  
Construction Algorithms ◽  
Concave Envelopes

It is difficult to extract the boundary of complex planar points with nonuniform distribution of point density, concave envelopes, and holes. To solve this problem, an algorithm is proposed in this paper. Based on Delaunay triangulation, the maximum boundary angle threshold is introduced as the parameter in the extraction of the rough boundary. Then, the point looseness threshold is introduced, and the fine boundary extraction is conducted for the local areas such as concave envelopes and holes. Finally, the complete boundary result of the whole point set is obtained. The effectiveness of the proposed algorithm is verified by experiments on the simulated point set and practical measured point set. The experimental results indicate that it has wider applicability and more effectiveness in engineering applications than the state-of-the-art boundary construction algorithms based on Delaunay triangulation.

Convex and concave envelopes: Revisited and new perspectives

2017 ◽  
Vol 45 (5) ◽  
pp. 421-426 ◽  
Author(s):  
Walid Ben-Ameur ◽  
Adam Ouorou ◽  
Guanglei Wang
Keyword(s):  
Concave Envelopes
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