High-quality bilingual dictionaries are very useful, but such resources are rarely available for lower-density language pairs, especially for those that are closely related. Using a third language to link two other languages is a well-known solution and usually requires only two input bilingual dictionaries A-B and B-C to automatically induce the new one, A-C. This approach, however, has never been demonstrated to utilize the complete structures of the input bilingual dictionaries, and this is a key failing because the dropped meanings negatively influence the result. This article proposes a constraint approach to pivot-based dictionary induction where language A and C are closely related. We create constraints from language similarity and model the structures of the input dictionaries as a Boolean optimization problem, which is then formulated within the Weighted Partial Max-SAT framework, an extension of Boolean Satisfiability (SAT). All of the encoded CNF (Conjunctive Normal Form), the predominant input language of modern SAT/MAX-SAT solvers, formulas are evaluated by a solver to produce the target (output) bilingual dictionary. Moreover, we discuss alternative formalizations as a comparison study. We designed a tool that uses the Sat4j library as the default solver to implement our method and conducted an experiment in which the output bilingual dictionary achieved better quality than the baseline method.