(eng): The incremental energy minimization approach is a compact variational formulation of the evolutionary boundary value problem for constitutive models of materials with a rate-independent response. Although it can be easily applied to many conventional models, its main advantages arise when applied to models with multiple strongly coupled dissipation mechanisms, where the direct construction of the coupled yield conditions and flow rules may be challenging. However, this usually requires a more complex numerical treatment of the resulting sequence of time-incremental boundary value problems resolved via the finite element method. This contribution presents, compares and discusses two genuine minimization approaches - the staggered solution procedure relying on alternating minimization and the monolithic approach employing global minimization - for an advanced constitutive model of shape memory alloys.