Abstract
We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is\(\left[ {\begin{array}{*{20}c} { - D^{ - 2} } & {A^T } \\ A & 0 \\ \end{array} } \right]\) instead of reducing to obtain the usualAD 2 A T system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the productAD 2 A T whenA has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only thatD be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.
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Vanderbei, R.J., Carpenter, T.J. Symmetric indefinite systems for interior point methods. Mathematical Programming 58, 1–32 (1993). https://doi.org/10.1007/BF01581257
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DOI: https://doi.org/10.1007/BF01581257