Continuous constrained optimization is a powerful tool for synthesizing novel human motion segments that are short. Graph-based motion synthesis methods such as motion graphs and move trees are popular ways to synthesize long motions by playing back a sequence of existing motion segments. However, motion graphs only support transitions between similar frames, and move trees only support transitions between the end of one motion segment and the start of another. In this paper, we introduce an optimization-based graph that combines continuous constrained optimization with graph-based motion synthesis. The constrained optimization is used to create a vast number of complex realistic-looking transitions in the graph. The graph can then be used to synthesize long motions with non-trivial transitions that for example allow the character to switch its behavior abruptly while retaining motion naturalness. We also propose to build this graph semi-autonomously by requiring a user to classify ge...