Abstract
Newton method is a classic and powerful method in continuous nonlinear optimization. However in this chapter, we introduce its counterpart in combinatorial optimization: discrete Newton method, and show that there exists a strong polynomial time algorithm for finding the root of a piecewise linear decreasing function, where the number of pieces is exponential. Then we show how to apply it in solving linear fractional combinatorial optimization problem, inverse combinatorial problem, and bottleneck expansion problem.
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Zhang, Z., Huang, X. (2019). Discrete Newton Method. In: Du, DZ., Pardalos, P., Zhang, Z. (eds) Nonlinear Combinatorial Optimization. Springer Optimization and Its Applications, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-030-16194-1_2
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DOI: https://doi.org/10.1007/978-3-030-16194-1_2
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