In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution o...In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.展开更多
This study analyzes the sensitivity analysis using shadow price of plastic products. This is based on a research carried out to study optimization problem of BOPLAS, a plastic industry in Maiduguri, North eastern Nige...This study analyzes the sensitivity analysis using shadow price of plastic products. This is based on a research carried out to study optimization problem of BOPLAS, a plastic industry in Maiduguri, North eastern Nigeria. Simplex method of Linear programming is employed to formulate the equations which were solved by using costenbol software. Sensitivity analysis using shadow price reveals that the price of wash hand bowls is critical to the net benefit (profit) of the company.展开更多
Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functi...Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions(KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains.Later, Bai et al.(SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche(Filomat. 34(12):3957–3969, 2020;Acta Math. Sin.(Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite program(ming(SD)P). They( establishe)d that the iteration complexities of algorithms based on their proposed KFs are O(n2/3log(n/ε) and O(n3/4log(n/ε)) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log(n/ε)) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.展开更多
文摘In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.
文摘This study analyzes the sensitivity analysis using shadow price of plastic products. This is based on a research carried out to study optimization problem of BOPLAS, a plastic industry in Maiduguri, North eastern Nigeria. Simplex method of Linear programming is employed to formulate the equations which were solved by using costenbol software. Sensitivity analysis using shadow price reveals that the price of wash hand bowls is critical to the net benefit (profit) of the company.
文摘Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions(KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains.Later, Bai et al.(SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche(Filomat. 34(12):3957–3969, 2020;Acta Math. Sin.(Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite program(ming(SD)P). They( establishe)d that the iteration complexities of algorithms based on their proposed KFs are O(n2/3log(n/ε) and O(n3/4log(n/ε)) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log(n/ε)) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.
