Extension of Karmarkar’s algorithm onto convex quadratically constrained quadratic problems

Extension of Karmarkar’s algorithm onto convex quadratically constrained quadratic problems

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Article ID: iaor19972084
Country: Netherlands
Volume: 72
Issue: 3
Start Page Number: 273
End Page Number: 289
Publication Date: Mar 1996
Journal: Mathematical Programming (Series A)
Authors: ,
Keywords: interior point methods
Abstract:

Convex quadratically constrained quadratic problems are considered. It is shown that such problems can be transformed to a conic form. The feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane (the analogue of a simplex), and a linear subspace. For a problem of such form, the analogue of Karmarkar’s projective transformation and logarithmic barrier function are built. This allows us to extend ‘word by word’ the method of Karmarkar for linear programming to quadratically constrained quadratic problems and allows us to obtain a similar polynomial worst-case bound for the number of iterations.

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