Reverse Convex Optimization, Reverse convex programming

2012 ◽  
Keyword(s):  
Convex Optimization ◽  
Convex Programming ◽  
Reverse Convex Programming ◽  
Reverse Convex

Comments on a reverse convex programming algorithm

1994 ◽  
Vol 5 (1) ◽  
pp. 95-96 ◽  
Author(s):  
S. Bensaad ◽  
S. E. Jacobsen
Keyword(s):  
Convex Programming ◽  
Programming Algorithm ◽  
Reverse Convex Programming ◽  
Reverse Convex

scholarly journals A formulation of combinatorial auction via reverse convex programming

2005 ◽  
Vol 2005 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Henry Schellhorn
Keyword(s):  
Convex Programming ◽  
Contraction Mapping ◽  
Combinatorial Auctions ◽  
Combinatorial Auction ◽  
Continuous Approximation ◽  
Reverse Convex Programming ◽  
Maximum Price ◽  
Programming Techniques ◽  
Np Hard Problem ◽  
Reverse Convex

In combinatorial auctions, buyers and sellers bid not only for single items but also for combinations (or “bundles”, or “baskets”) of items. Clearing the auction is in general an NP-hard problem; it is usually solved with integer linear programming. We proposed in an earlier paper a continuous approximation of this problem, where orders are aggregated and integrality constraints are relaxed. It was proved that this problem could be solved efficiently in two steps by calculating two fixed points, first the fixed point of a contraction mapping, and then of a set-valued function. In this paper, we generalize the problem to incorporate constraints on maximum price changes between two auction rounds. This generalized problem cannot be solved by the aforementioned methods and necessitates reverse convex programming techniques.

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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