摘要
On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.
On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called 'central- path' for linear programming, we propose a new framework of primal-dual in feasible interior-point method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results; (a) if the homotopy parameter ft can not reach to zero, then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x^(0) , we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x (0), we can obtain a E-solution; and (d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve .r(μ), which towards to the generalized solutions.
