Optimization Letters
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Published By Springer-Verlag

1862-4480, 1862-4472

Author(s):  
Giandomenico Mastroeni ◽  
Letizia Pellegrini ◽  
Alberto Peretti

Author(s):  
Manuel Radons ◽  
Siegfried M. Rump

AbstractLet A be a real $$n\times n$$ n × n matrix and $$z,b\in \mathbb R^n$$ z , b ∈ R n . The piecewise linear equation system $$z-A\vert z\vert = b$$ z - A | z | = b is called an absolute value equation. In this note we consider two solvers for uniquely solvable instances of the latter problem, one direct, one semi-iterative. We slightly extend the existing correctness, resp. convergence, results for the latter algorithms and provide numerical tests.


Author(s):  
Tobias Lehmann ◽  
Max-K. von Renesse ◽  
Alexander Sambale ◽  
André Uschmajew

AbstractWe derive an a priori parameter range for overrelaxation of the Sinkhorn algorithm, which guarantees global convergence and a strictly faster asymptotic local convergence. Guided by the spectral analysis of the linearized problem we pursue a zero cost procedure to choose a near optimal relaxation parameter.


Author(s):  
John Martinovic ◽  
Nico Strasdat ◽  
José Valério de Carvalho ◽  
Fabio Furini

AbstractThe aim of this letter is to design and computationally test several improvements for the compact integer linear programming (ILP) formulations of the temporal bin packing problem with fire-ups (TBPP-FU). This problem is a challenging generalization of the classical bin packing problem in which the items, interpreted as jobs of given weight, are active only during an associated time window. The TBPP-FU objective function asks for the minimization of the weighted sum of the number of bins, viewed as servers of given capacity, to execute all the jobs and the total number of fire-ups. The fire-ups count the number of times the servers are activated due to the presence of assigned active jobs. Our contributions are effective procedures to reduce the number of variables and constraints of the ILP formulations proposed in the literature as well as the introduction of new valid inequalities. By extensive computational tests we show that substantial improvements can be achieved and several instances from the literature can be solved to proven optimality for the first time.


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