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Warm-start cuts for Generalized Benders Decomposition

Jakub Kůdela, Pavel Popela (2017)

Kybernetika

In this paper, we describe a decomposition algorithm suitable for two-stage convex stochastic programs known as Generalized Benders Decomposition. For this algorithm we propose a new reformulation that incorporates a lower bound cut that serves as a warm-start, decreasing the overall computation time. Additionally, we test the performance of the proposed reformulation on two modifications of the algorithm (bunching and multicut) using numerical examples. The numerical part is programmed in MATLAB...

Weaker convergence conditions for the secant method

Ioannis K. Argyros, Saïd Hilout (2014)

Applications of Mathematics

We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.

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