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- W2054501360 abstract "We present an algorithm for the quadratic zero-one minimization by reformulation of the problem into an equivalent concave quadratic minimization. We then specialize an algorithm proposed by Kalantari and Rosen [13], which globally minimizes a concave quadratic function over arbitrary polytopes. The algorithm exploits the special structure of the problem. Given a set of conjugate directions to the Hessian, we construct a linear convex envelope over a “tight” containing parallelopiped, by solving 2n linear programs each solvable in O(n) time, n being the dimension of the problem. A bound on the maximum difference in the value of the quadratic function and the convex envelope may be obtained, which provides a global measure of underestimation. A branch-and-bound method is presented in which subproblems are defined by fixing a variable at zero or one. For each subproblem, we obtain a lower bound by minimizing the linear convex envelope over the feasible region of the subproblem. Computational experience with the algorithm is also presented." @default.
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- W2054501360 date "1990-08-01" @default.
- W2054501360 modified "2023-10-14" @default.
- W2054501360 title "An algorithm for quadratic zero-one programs" @default.
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- W2054501360 doi "https://doi.org/10.1002/1520-6750(199008)37:4<527::aid-nav3220370407>3.0.co;2-p" @default.
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