Linear programs with an additional rank two reverse convex constraint

1994 ◽  
Vol 4 (4) ◽  
pp. 441-454 ◽  
Author(s):  
Ulrich Pferschy ◽  
Hoang Tuy
Keyword(s):  
Linear Programs ◽  
Convex Constraint ◽  
Reverse Convex

Linear programs with an additional reverse convex constraint

1980 ◽  
Vol 6 (1) ◽  
pp. 257-269 ◽  
Author(s):  
Richard J. Hillestad ◽  
Stephen E. Jacobsen
Keyword(s):  
Linear Programs ◽  
Convex Constraint ◽  
Reverse Convex

scholarly journals Reverse convex problems: an approach based on optimality conditions

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Ider Tseveendorj
Keyword(s):  
Optimality Conditions ◽  
Linear Program ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Convex Constraint ◽  
Convergence Of An Algorithm ◽  
Convex Problems ◽  
Reverse Convex

We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.

scholarly journals A Global Optimization Approach for Solving Generalized Nonlinear Multiplicative Programming Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Lin-Peng Yang ◽  
Pei-Ping Shen ◽  
Yong-Gang Pei
Keyword(s):  
Global Optimization ◽  
Programming Problem ◽  
Convex Programming ◽  
Optimization Approach ◽  
Linear Programs ◽  
Convex Programming Problem ◽  
Multiplicative Programming ◽  
Main Work ◽  
Reverse Convex Programming ◽  
Reverse Convex

This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on an equivalently reverse convex programming problem. As a result, in the computation procedure the main work is solving a series of linear programs that do not grow in size from iterations to iterations. Further several key strategies are proposed to enhance solution production, and some of them can be used to solve a general reverse convex programming problem. Numerical results show that the computational efficiency is improved obviously by using these strategies.

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