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.

This paper explores whether analog circuitry can adequately perform constrained optimization. Constrained optimization circuits are designed using the differential multiplier method. These circuits fulfill time-varying constraints correctly. Example circuits include a quadratic programming circuit and a constrained flip-flop.

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).

This paper explores whether analog circuitry can adequately perform constrained optimization. Constrained optimization circuits are designed using the differential multiplier method. These circuits fulfill time-varying constraints correctly. Example circuits include a quadratic programming circuit and a constrained flip-flop.

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).

This paper explores whether analog circuitry can adequately perform constrainedoptimization. Constrained optimization circuits are designed using the differential multiplier method.

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).

I concentrate on this class of design 1989) that lays out the relation problems in this article. An example of an implicit function mapping from behavior to structure), typically in many engineering devices is safety: For conducted by means of a search or exploration example, a subsystem's role might only be in the space of possible subassemblies explained as something that prevents the of components. This accent on assembly is in leakage of a potentially hazardous substance, fact the origin of the frequent suggestion that and this function might never be explicitly design is a synthetic task. Only a vanishingly design specifications will usually mention a small number of objects in this space constitute number of constraints. The distinction even satisficing, not to mention optimal, between functions and constraints is hard to solutions. What is needed to make design formally pin down; functions are constraints practical are strategies that radically shrink on the behavior or properties of the device. However, it is useful to distinguish functions Set against the view of design as a deliberative from other constraints because functions are problem-solving process is the view of the primary reason that the device is desired. Artistic creations and weigh more than..."), the process of making scientific theories are often said by their creators the artifact from its description (manufacturability to have occurred to them in this Even when a plausible solution itself (for example, "I want a design within a occurs in this way, the proposal still needs to week"), and so on.