Mihály Csaba Markót

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We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The results are published in two papers, the first one contains the theoretical investigations on the convergence(More)
The paper presents a new verified optimization method for the problem of finding the densest packings of non-overlapping equal circles in a square. In order to provide reliable numerical results, the developed algorithm is based on interval analysis. As one of the most efficient parts of the algorithm, an interval-based version of a previous elimination(More)
In the paper we deal with lower bounds constructed for the asymptotic competitive ratio of semi-online bin packing and batched bin packing algorithms.We determine the bounds as the solutions of a related nonlinear optimization problem using theoretical analysis and a reliable numerical global optimization method. Our results improve the lower bounds given(More)
The paper is dealing with the problem of finding the densest packings of equal circles in the unit square. Recently, a global optimization method based exclusively on interval arithmetic calculations has been designed for this problem. With this method it became possible to solve the previously open problems of packing 28, 29, and 30 circles in the(More)
The algorithmic differentiation in the COCONUT Environment does not only provide point evaluations but also range enclosures of derivatives up to order 3, as well as slopes up to second order. Care is taken to ensure that rounding errors are treated correctly. The ranges of the enclosures can be tightened by combining the evaluation routines with constraint(More)
We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The convergence properties of the multisplitting methods, an important class of multisection procedures are investigated(More)
The paper deals with the problem class of finding the densest packings of non-overlapping equal circles within a unit square. We introduce a new interval branch-and-bound algorithm designed specifically for this optimization problem. After a brief description of the applied algorithmic tools, the capabilities of the algorithm are shown by solving the(More)
We compare six state-of-the-art local optimization solvers with focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check indicator (measuring whether the local minimizers found are good candidates for near-optimal verified feasible(More)