• East Asian mathematical journal
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• v.35 no.5
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• pp.597-612
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• 2019

In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.429-439
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• 1995

The Interior point method in linear programming is classified into two categories the affine-scaling method and the logarithmic barrier method. In this paper, we integrate those methods and implement them in one shared module. First, we analyze the procedures of two interior point methods and then find a unified formula in finding directions to improve the current solution and conditions to terminate the procedure. Second, we build the shared modules which can be used in each interior point method. Then these modules are experimented in NETLIB problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.41-53
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• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.