Global Optimization and Parallel Processing of Nonlinear Problems in Engineering Applications

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The objective of this project is to develop an efficient nonlinear optimization method - NOVEL: Nonlinear Optimization Via External Lead - and the supporting hardware/software to solve large-scale nonlinear optimization problems in operations research, digital signal processing, and neural-network learning. Such a method will allow many important application problems in these areas to be solved better as well as faster than existing methods. The method first transforms nonlinear constrained optimization problems using Lagrange multipliers into unconstrained optimization problems. This transformation allows both constrained and unconstrained problems to be solved in a unified framework. The key idea of the method is to use a user-defined trace to pull a search out of a local optimum (a local saddle point in constrained optimization and a local minimum in unconstrained optimization) without having to restart it from a new starting point. The proposed method has a good balance between global search and local search. In global search, NOVEL relies on two counteracting forces: local gradient information that drives the search to a local optimum, and a deterministic trace that leads the search out of a local optimum once it gets there. The effect of the trace on the search trajectory is expressed in terms of the distance between the current position of the trajectory and that of the trace. Good starting points identified in the global-search phase are then searched more extensively using pure local searches. The proposed research consists of four aspects: refinement of the NOVEL method, parallel processing, extension to mixed-nonlinear optimization problems, and applications of the methods developed to solve problems in operations research, digital signal processing, and neural-network learning.