Subproblem and Overall Convergence for a Method-of-Centers Algorithm

This paper considers convergence of a method-of-centers algorithm for solving nonlinear programming problems. An upper bound is derived for the number of steps needed to solve each subproblem, defined by the algorithm, when the method of steepest ascent is employed. Also, an upper bound is found for the total number of subproblem steps needed to solve all of the subproblems required to find a feasible point having an objective value with a prescribed maximum deviation from the optimal value.