A unified feasible direction interior approach to the minimization of linear and general objective functions subject to linear constraints

A unified feasible direction interior approach to the minimization of linear and general objective functions subject to linear constraints

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Article ID: iaor19932419
Country: South Africa
Volume: 8
Start Page Number: 90
End Page Number: 107
Publication Date: Nov 1992
Journal: Orion
Authors: ,
Keywords: interior point methods
Abstract:

A modification of Snyman’s interior feasible direction method for linear programming is proposed and the method is also extended to problems where the objective function is non-linear. The method attempts to identify the optimal bounding set of active constraints. In the modified algorithm the successive interior steps in the identifying cycle are no longer constrained to be in the plane of constant objective function value, but are computed to ensure improvement in the objective function for any non-zero step taken within the cycle. The method is also extended to non-linear objective functions by allowing for line searches within the interior and along bounding hypersurfaces. A formal unified algorithm is presented and the method is illustrated by its successful application to a number of simple problems from different categories.

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