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We present a mixed-integer linear program (MILP), a cutting plane algorithm, and a column-and-cut algorithm.

Subsequently, we solve the problem in the dual domain by means of the cutting plane algorithm, and finally, we perform the primal reconstruction.

We develop cutting-plane algorithms and several heuristic approaches for solving the two models.

Therefore, advanced optimization concepts like column generation and cutting plane algorithms are used.

For more detailed information on cutting plane algorithms, we refer to[27].

In the context of MILP, cutting plane algorithms are mostly used to solve the linear relaxation of MILPs.

This section presents analytic center cutting plane algorithms for solving a strongly pseudomonotone variational inequality (mathit{VI}[F, X]) whose domain is an unbounded convex body.

Joachims et al. [3] has demonstrated that 1-slack cutting plane algorithms are equivalent to but substantially faster than -slack ones on a wide range of problems.

We present some analytic center cutting plane algorithms that extend the algorithms proposed in [1, 2, 16], from polytopes/polyhedron to convex regions, or from bounded convex region to unbounded convex regions.

We develop an iterative primal-dual algorithm and a cutting plane algorithm to solve the problem and provide preliminary computational results on a network up to nine masses.

Then the network design problem is solved by a cutting plane algorithm based on these inequalities and using a compact formulation issued from the transversality of the bicircular matroid.

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