Least-norm linear programming solution as an unconstrained minimization problem |
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Authors: | OL Mangasarian |
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Institution: | Mathematics Research Center, University of Wisconsin-Madison, Madison, Wisconsin 53706 USA |
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Abstract: | It is shown that the dual of the problem of minimizing the 2-norm of the primal and dual optimal variables and slacks of a linear program can be transformed into an unconstrained minimization of a convex parameter-free globally differentiable piecewise quadratic function with a Lipschitz continuous gradient. If the slacks are not included in the norm minimization, one obtains a minimization problem with a convex parameter-free quadratic objective function subject to nonnegativity constraints only. |
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