In this paper, a new neural architecture, the multisynapse neural network, is developed for constrained optimization problems, whose objective functions may include high-order, logarithmic, and sinusoidal forms, etc., unlike the traditional Hopfield networks which can only handle quadratic form optimization. Meanwhile, based on the application of this new architecture, a fuzzy bidirectional associative clustering network (FBACN), which is composed of two layers of recurrent networks, is proposed for fuzzy-partition clustering according to the objective-functional method. It is well known that fuzzy c-means is a milestone algorithm in the area of fuzzy c-partition clustering. All of the following objective-functional-based fuzzy c-partition algorithms incorporate the formulas of fuzzy c-means as the prime mover in their algorithms. However, when an application of fuzzy c-partition has sophisticated constraints, the necessity of analytical solutions in a single iteration step becomes a fatal issue of the existing algorithms. The largest advantage of FBACN is that it does not need analytical solutions. For the problems on which some prior information is known, we bring a combination of part crisp and part fuzzy clustering in the third optimization problem.