Minimizing the Absolute Value Energy Function: An Application to Geometrical Constraint-Solving
This paper proposes a new connectionist model to minimize the absolute value energy function based on the Boltzmann machine. In conventional models, n th-order constraints (nonlinear optimization problems) are solved by minimizing the 2n thorder energy function, which brings forth explosive increase of the number of units and connections among them. By using the absolute value energy function, n th-order constraints can be directly represented by the n th-order energy function. Hence, a very great reduction of the network complexity becomes possible. Our model is particularly suited for applications, such as geometrical constraint-solving, in which nonlinearity plays a definitive role.
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