Relative interior and closure of the set of inner points

2019 ◽  
Vol 43 (5-6) ◽  
pp. 761-772
Author(s):  
F.J. García-Pacheco
Keyword(s):  
Relative Interior

scholarly journals On finding a point in the relative interior of a polyhedral set and degeneracy in geometric programming

1978 ◽  
Vol 20 (4) ◽  
pp. 487-494 ◽  
Author(s):  
T. R. Jefferson ◽  
C. H. Scott
Keyword(s):  
Objective Function ◽  
Geometric Programming ◽  
Dual Problem ◽  
Optimization Theory ◽  
Inequality Constraints ◽  
Linear Constraints ◽  
Relative Interior ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Nonlinear Objective Function

AbstractGeometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

Regularity Conditions via Quasi-Relative Interior in Convex Programming

2008 ◽  
Vol 19 (1) ◽  
pp. 217-233 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Gert Wanka
Keyword(s):  
Convex Programming ◽  
Relative Interior ◽  
Regularity Conditions ◽  
Quasi Relative Interior

The relative interior of the base polyhedron and the core

2001 ◽  
Vol 18 (3) ◽  
pp. 635-648 ◽  
Author(s):  
Jingang Zhao
Keyword(s):  
Relative Interior ◽  
The Core

scholarly journals A mobile mapping system utilizing a spherical camera

2021 ◽  
Author(s):  
Craig Alleva
Keyword(s):  
Data Acquisition ◽  
Survey Methods ◽  
Relative Interior ◽  
Attractive Alternative ◽  
Single Camera ◽  
Exterior Orientation ◽  
Camera System ◽  
Mobile Data ◽  
Highway Management ◽  
Spherical Camera

The transportation departments belonging to respective provinces currently collect highway management data with the use of several methods and systems which include visual field inspections, survey methods, aerial photogrammetry, as well as mobile data acquisition systems. Spherical cameras offer an attractive alternative to standard mobile data acquisition devices for highway management systems as they provide full coverage with a single camera. Inclusion of such a camera requires methods of determining relative, interior and exterior orientation information, as well as bore-sight and lever arm determination. Specialized methods of mosaicking[sic] the imagery are also required. This paper focuses on exploring these methods for spherical cameras. Several computer programs were developed to solve for relative, interior, and exterior orientation parameters. It was concluded that a spherical camera can be efficiently utilized for highway data collection and provides full data coverage with a single camera system.

Topological Approaches to the Second Type of Covering-Based Rough Sets

2011 ◽  
Vol 204-210 ◽  
pp. 1781-1784
Author(s):  
Bin Chen
Keyword(s):  
Data Mining ◽  
Information Systems ◽  
Rough Sets ◽  
Relative Interior ◽  
Upper Approximation ◽  
Definition Of ◽  
The Relationship

Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies covering-based rough sets from the topological view. We explore the relationship between the relative closure and the second type of covering upper approximation. The major contributions of this paper are that we use the definition of the relative closure and the relative interior to discuss the conditions under which the relative operators satisfy certain classical properties. The theorems we get generalize some of the results in Zhu’s paper.

scholarly journals Spatial Stit Tessellations: Distributional Results for I-Segments

2012 ◽  
Vol 44 (3) ◽  
pp. 635-654 ◽  
Author(s):  
Christoph Thäle ◽  
Viola Weiss ◽  
Werner Nagel
Keyword(s):  
Cell Division ◽  
Explicit Formula ◽  
Three Dimensional ◽  
Relative Interior ◽  
Construction Process ◽  
Face To Face ◽  
Random Tessellations ◽  
Insight Into

In this paper we consider three-dimensional random tessellations that are stable under iteration (STIT tessellations). STIT tessellations arise as a result of subsequent cell division, which implies that their cells are not face-to-face. The edges of the cell-dividing polygons are the so-called I-segments of the tessellation. The main result is an explicit formula for the distribution of the number of vertices in the relative interior of the typical I-segment. In preparation for its proof, we obtain other distributional identities for the typical I-segment and the length-weighted typical I-segment, which provide new insight into the spatiotemporal construction process.

scholarly journals Spatial Stit Tessellations: Distributional Results for I-Segments

2012 ◽  
Vol 44 (03) ◽  
pp. 635-654 ◽  
Author(s):  
Christoph Thäle ◽  
Viola Weiss ◽  
Werner Nagel
Keyword(s):  
Cell Division ◽  
Explicit Formula ◽  
Three Dimensional ◽  
Relative Interior ◽  
Construction Process ◽  
Face To Face ◽  
Random Tessellations ◽  
Insight Into

In this paper we consider three-dimensional random tessellations that are stable under iteration (STIT tessellations). STIT tessellations arise as a result of subsequent cell division, which implies that their cells are not face-to-face. The edges of the cell-dividing polygons are the so-called I-segments of the tessellation. The main result is an explicit formula for the distribution of the number of vertices in the relative interior of the typical I-segment. In preparation for its proof, we obtain other distributional identities for the typical I-segment and the length-weighted typical I-segment, which provide new insight into the spatiotemporal construction process.

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