A Hierarchical Method for Solving Soft Nonlinear Constraints

Constraints that express relationships among objects are used to model and solve various problems arising from fields such as artificial intelligence, software, and computer graphics. Soft constraints are often important for applications that involve complex relationships among objects. This paper proposes a new method for solving soft constraints. The method treats soft nonlinear con- straints with hierarchical preferences, and computes solutions that satisfy as many constraints with strong preferences as possible. It adopts the method of Lagrange multipliers to enable the accurate computation of local solutions. The paper also presents the result of a preliminary experiment using a simple geometric example.