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An Algorithm for Finding the Generalized Chebyshev Center of Sets Defined via Their Support Functions

Abstract

This paper is dedicated to an optimization problem. Let A, B subset of R-n be compact convex sets. Consider the minimal number t(0) > 0 such that t(0)B covers A after a shift to a vector x(0) is an element of R-n. The goal is to find t(0) and x(0). In the special case of B being a unit ball centered at zero, x(0) and t(0) are known as the Chebyshev center and the Chebyshev radius of A. This paper focuses on the case in which A and B are defined with their black-box support functions. An algorithm for solving such problems efficiently is suggested. The algorithm has a superlinear convergence rate, and it can solve hundred-dimensional test problems in a reasonable time, but some additional conditions on A and B are required to guarantee the presence of convergence. Additionally, the behavior of the algorithm for a simple special case is investigated, which leads to a number of theoretical results. Perturbations of this special case are also studied.

article Article

date_range 2024

language English

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Arkhipov P.

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optimization

Chebyshev center

gradient descent

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Effect of corrosion on flexural strength of reinforced concrete beams with polypropylene fibers

Abstract

An experimental study was performed to investigate the effects of polypropylene fibers on uncorroded and corroded reinforced concrete beams. Three different volume fractions of polypropylene fibers having 0, 0.5, and 1.5%, were tested at four corrosion levels of 0% and approximately 5, 7, and 9%. A full scale of an accelerated corrosion pool was used for the accelerated corrosion process. Reinforced concrete beams were used for an under monotonic bending test. The contribution of the actual corrosion levels of transverse and longitudinal reinforcement bars to the total corrosion levels were obtained from reinforcement bars fully extracted from concrete. Flexural strength, bond-slip, and moment-curvature relationships were examined for uncorroded and corroded reinforced concrete beams. A new model was developed to predict the flexural strength of corroded reinforced concrete beams. The proposed model for predicting the residual flexural strength of corroded beams was compared with test data published in previous studies. Furthermore, a novel model is presented for improved predictions between the actual and theoretically estimated corrosion mass losses, based on Faraday’s law, with the aid of fully extracted reinforcement bars. The model used to predict the flexural strength of corroded reinforced concrete beams with large sizes demonstrated good agreement with current and previously published literature data. In the case of corroded beams comprising differing amounts of polypropylene fibers, the performance of the corroded beams was limited by a fiber volume fraction of 1.5% at low corrosion levels.

article Article

date_range 2018

language English

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