On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints

2015 ◽  
Vol 171 (2) ◽  
pp. 617-642 ◽  
Author(s):  
Nguyen Thi Van Hang ◽  
Nguyen Dong Yen
Keyword(s):  
Convex Functions ◽  
Linear Constraints ◽  
Polyhedral Convex ◽  
Polyhedral Convex Functions

scholarly journals Extension of M-Convexity and L-Convexity to Polyhedral Convex Functions

2000 ◽  
Vol 25 (4) ◽  
pp. 352-427 ◽  
Author(s):  
Kazuo Murota ◽  
Akiyoshi Shioura
Keyword(s):  
Convex Functions ◽  
Polyhedral Convex ◽  
Polyhedral Convex Functions

A finite algorithm for the rank regression problem

1982 ◽  
Vol 19 (A) ◽  
pp. 241-252
Author(s):  
M. R. Osborne
Keyword(s):  
Convex Functions ◽  
Numerical Results ◽  
Regression Problem ◽  
New Approach ◽  
Rank Regression ◽  
Polyhedral Convex ◽  
Polyhedral Convex Functions

A new approach to the minimization of polyhedral convex functions is applied to give a finite algorithm for the rank regression problem. Numerical results for the Daniel and Wood example are presented.

A finite algorithm for the rank regression problem

1982 ◽  
Vol 19 (A) ◽  
pp. 241-252 ◽  
Author(s):  
M. R. Osborne
Keyword(s):  
Convex Functions ◽  
Numerical Results ◽  
Regression Problem ◽  
New Approach ◽  
Rank Regression ◽  
Polyhedral Convex ◽  
Polyhedral Convex Functions

A new approach to the minimization of polyhedral convex functions is applied to give a finite algorithm for the rank regression problem. Numerical results for the Daniel and Wood example are presented.

scholarly journals On two problems over polyhedral convex sets

2015 ◽  
Vol 1 (1) ◽  
pp. 9-15
Author(s):  
Tran Vu Thieu
Keyword(s):  
Convex Sets ◽  
Convex Set ◽  
Linear Constraints ◽  
Concave Programming ◽  
Linear Equality ◽  
Polyhedral Convex ◽  
Polyhedral Convex Sets ◽  
Polyhedral Convex Set

In this paper, we are concerned with the following two problems often encountered in concave programming: Given the  vertices and extreme detections of a polyhedral convex set Modefined by a system of linear constraints, determine the vertices and  extreme directions of the polyhedral convex set  obtained from M just by adding one new linear equality (or inequality) constraint.Among the constraints of a given polyhedral convex set, find those which are redundant, i.e. which can be removed without affecting the polyhedral convex set.

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