Protein alignment is a challenging applied optimization problem. Superposition methods are based on the maximization of a score function with respect to rigid-body modifications of relative positions. The problem of score maximization can be modelled as a continuous nonsmooth optimization problem (low order-value optimization (LOVO)). This allows one to define practical and convergent methods that produce monotone increases of the score. In this paper, trust-region methods are introduced for solving the problem. Numerical results are presented. Computer software related to the LOVO approach for protein alignment is available at www.ime.unicamp.br/ similar to martinez/lovoalign.284690710