An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and twosided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in somemathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.