This paper compares the performance of penalty and Lagrange multiplier approaches for the necessary unit-length constraint in the computation of liquid crystal equilibrium configurations. Building on previous work in [SIAM J. Sci. Comput., 37 (2015), pp. S157--S176; SIAM J. Numer. Anal., 53 (2015), pp. 2226--2254], the penalty method is derived and well-posedness of the linearizations within the nonlinear iteration is discussed. In addition, the paper considers the effects of tailored trust-region methods in the context of finite-element discretizations and nested iteration for both formulations. Such methods are aimed at increasing the efficiency and robustness of each algorithm's nonlinear iterations. Three representative elastic equilibrium problems are considered to examine each method's performance. The first two configurations have analytical expressions for their exact solutions and, therefore, convergence to the true solution is considered. The third problem considers complicated boundary conditio...
['James H. Adler', 'D. B. Emerson', 'Scott MacLachlan', 'Thomas A. Manteuffel']
CONSTRAINED OPTIMIZATION FOR LIQUID CRYSTAL EQUILIBRIA