Interior-point algorithms are among the most efficient techniques for solving complementarity problems. In this paper, a procedure for globalizing interior-point algorithms by using the maximum stepsize is introduced. The algorithm combines exact or inexact interior-point and projected-gradient search techniques and employs a line-search procedure for the natural merit function associated with the complementarity problem. For linear problems, the maximum stepsize is shown to be acceptable if the Newton interior-point search direction is employed. Complementarity and optimization problems are discussed, for which the algorithm is able to process by either finding a solution or showing that no solution exists. A modification of the algorithm for dealing with infeasible linear complementarity problems is introduced which, in practice, employs only interior-point search directions. Computational experiments on the solution of complementarity problems and convex programming problems by the new algorithm are included.574457485