On the Convergence of Some Feasible Direction Algorithms for Nonlinear Programming

1967 ◽  
Vol 5 (2) ◽  
pp. 268-279 ◽  
Author(s):  
Donald M. Topkis ◽  
Arthur F. Veinott, Jr.
Keyword(s):  
Nonlinear Programming ◽  
Feasible Direction ◽  
Feasible Direction Algorithms

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1988 ◽  
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Efficient Algorithm ◽  
Optimization Method ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

Abstract The Feasible Direction Method of Zoutendijk has proven to be one of the efficient algorithm currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of having equality type constraints, there does not exist nonzero direction close to the feasible region, the traditional algorithm can not work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1989 ◽  
Vol 111 (3) ◽  
pp. 442-445
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Optimization Method ◽  
Direction Finding ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

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