Convex programs with an additional reverse convex constraint

1987 ◽  
Vol 52 (3) ◽  
pp. 463-486 ◽  
Author(s):  
H. Tuy
Keyword(s):  
Convex Programs ◽  
Convex Constraint ◽  
Reverse Convex

Ultimate and Practical Limits for Counterweight Balancing of Six-Bar Linkages

2006 ◽  
Author(s):  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Great Efficiency ◽  
Convex Programs ◽  
Local Optima ◽  
Trade Off ◽  
Convex Constraint ◽  
Main Challenge ◽  
Dynamic Forces

The designer’s main challenge when counterweight balancing a linkage is to determine the counterweights that realize an optimal trade-off between the dynamic forces of interest. This problem is often formulated as an optimization problem that is generally nonlinear and therefore suffers from local optima. It has been shown earlier, however, that, through a proper parametrization of the counterweights, a convex program can be obtained. Convex programs are nonlinear optimization problems of which the global optimum is guaranteed to be found with great efficiency. The present paper extends this previous work in two respects: (i) the methodology is generalized from four-bar to planar N-bar (rigid) linkages and (ii) it is shown that requiring the counterweights to be realizable in practice can be cast as a convex constraint. Numerical results for a Watt six-bar linkage suggest much more balancing potential for six-bar linkages than for four-bar linkages.

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.

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