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951.
The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or
integer linear program. Traditional approaches to branching variable selection rely on estimating the effect of the candidate
variables on the objective function. We present a new approach that relies on estimating the impact of the candidate variables
on the active constraints in the current LP relaxation. We apply this method to the problem of finding the first feasible
solution as quickly as possible. Empirical experiments demonstrate a significant improvement compared to a state-of-the art
commercial MIP solver. 相似文献
952.
953.
Linear mixed 0–1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP)
problems. We exploit these equivalences to transpose the concept of mixed 0–1 Gomory cuts to BLP. The first phase of our new
algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination
with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria
are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate
the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of
randomly generated problems.
Work of the authors was partially supported by FCAR, MITACS and NSERC grants. 相似文献
954.
This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957. 相似文献
955.
S. Al-Homidan 《Journal of Optimization Theory and Applications》2007,135(3):583-598
Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the
problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead
of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain
exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an
inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned
conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm. 相似文献
956.
957.
958.
E. V. Suchilkina 《Journal of Mathematical Sciences》2007,147(1):6510-6516
At the end of the twentieth century, in mathematical physics, the Knizhnik-Zamolodchikov equations for the root systems A
n
and their generalizations for the root systems of types B
n
, C
n
, and D were constructed. For the root system of type G
2, the vector version of the Knizhnik-Zamolodchikov equations was obtained by M. P. Zamakhovskii and V. P. Leksin. However,
the tensor version of these equations has remained unstudied. In this paper, the Knizhnik-Zamolodchikov equations associated
with the root system of type G
2 are considered.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal
Conference-2004, Part 3, 2006. 相似文献
959.
960.