On the use of the quasi-relative interior in optimization

Optimization ◽  
2015 ◽  
Vol 64 (8) ◽  
pp. 1795-1823 ◽  
Author(s):  
C. Zălinescu
2008 ◽  
Vol 19 (1) ◽  
pp. 217-233 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Gert Wanka

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Capătă Adela Elisabeta

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.


2007 ◽  
Vol 50 (3) ◽  
pp. 605-610 ◽  
Author(s):  
F. Cammaroto ◽  
B. Di Bella

AbstractWe establish two separation theorems in which the classic interior is replaced by the quasi-relative interior.


Author(s):  
T. R. Jefferson ◽  
C. H. Scott

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.


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

2021 ◽  
Author(s):  
Craig Alleva

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.


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