This work discusses various optimization techniques which were proposed in models for controlling arm movements. In particular, the minimum-muscle-tension-change model is investigated. A dynamic simulator of the monkey's arm, including seventeen single and double joint muscles, is utilized to generate horizontal hand movements. The hand trajectories produced by this algorithm are discussed.

Analog hardware has obvious advantages in terms of its size, speed, cost, and power consumption. Analog chip designers, however, should not feel constrained to mapping existingdigital algorithms to silicon. Many times, new algorithms must be adapted or invented to ensure efficient implementation in analog hardware. Novel analog algorithms embedded in the hardware must be simple and obey the natural constraints of physics. Much algorithm intuition can be gained from experimenting with these continuous-time nonlinear systems. For example, the algorithm described in this paper arose from experimentation with existing analog segmentation hardware. Surprisingly,many of these "analog" algorithms may prove useful even if a computer vision researcher is limited to simulating the analog hardware on a digital computer [7] .

The computation consists of the following steps.

We present a new way to derive dissipative, optimizing dynamics from the Lagrangian formulation of mechanics. It can be used to obtain both standard and novel neural net dynamics for optimization problems. To demonstrate this we derive standard descent dynamics as well as nonstandard variants that introduce a computational attention mechanism.

The computation consists of the following steps.

We present a new way to derive dissipative, optimizing dynamics from the Lagrangian formulation of mechanics. It can be used to obtain both standard and novel neural net dynamics for optimization problems. To demonstrate this we derive standard descent dynamics as well as nonstandard variants that introduce a computational attention mechanism.

Images from left to right display the saliency map following the saliency and pairing stages and a number of strongest groups.

At the control level, distinctive places and distinctive travel edges are identified based on the interaction between the robot's control strategies, its sensorimotor system, and the world. A distinctive place is defined as the local maximum of a distinctiveness measure appropriate to its immediate neighborhood, and is found by a hill-climbing control strategy. A distinctive travel edge, similarly, is defined by a suitable measure and a path-following control strategy. The topological network description is created by linking the distinctive places and travel edges. Metrical information is then incrementally assimilated into local geometric descriptions of places and edges, and finally merged into a global geometric map.

Purdue University W. Lafayette, IN. 47907 ABSTRACT A nonlinear neural framework, called the Generalized Hopfield network, is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate GHNs implementing the three most important optimization algorithms, namely the Augmented Lagrangian, Generalized Reduced Gradient and Successive Quadratic Programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and which can gain from the introduction of nonlinearities in their structure (eg. The ability of networks of highly interconnected simple nonlinear analog processors (neurons) to solve complicated optimization problems was demonstrated in a series of papers by Hopfield and Tank (Hopfield, 1984), (Tank, 1986).

Purdue University Purdue University Purdue University W. Lafayette, IN. 47907 W. Lafayette, IN. 47907 W. Lafayette, IN. 47907 ABSTRACT A nonlinear neural framework, called the Generalized Hopfield network, is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate GHNs implementing the three most important optimization algorithms, namely the Augmented Lagrangian, Generalized Reduced Gradient and Successive Quadratic Programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and which can gain from the introduction of nonlinearities in their structure (eg. The ability of networks of highly interconnected simple nonlinear analog processors (neurons) to solve complicated optimization problems was demonstrated in a series of papers by Hopfield and Tank (Hopfield, 1984), (Tank, 1986).