Abstract
A new approach to the construction of lower bounds of quadratic function the permutation matrix set, based on the utilization of functional representations and convex extensions, is offered. Several quadratic functional representations of the are formed. A family of one-parametric convex quadratic extensions of a quadratic function from the set onto the Euclidean space is formed. The results can be applied in approximate and exact methods of quadratic optimization on the permutation matrix set.
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