Neurodynamic Approaches to Constrained Optimization with Generalized-Convex and Multiple-Objective Functions

Optimization is a ubiquitous phenomenon in nature and an important tool in science, engineering, and commerce. As the counterparts of biological neural systems, properly designed artificial neurodynamic systems can function as goalseeking computational models for solving optimization problems in a variety of settings. For dynamic optimization in many real-time applications, such neurodynamic approaches are more competent than conventional optimization methods because of the inherently parallel and distributed nature of neural information processing. The past three decades witnessed the birth and growth of neurodynamic optimization with various globally convergent recurrent neural networks developed. Nevertheless, almost all existing results are concerned with convex optimization problems with single objective functions and effective neurodynamic approach to constrained optimization with nonconvex or multiple-objective functions is rarely available. In numerous applications, the objective functions to be minimized are not necessarily convex. The nonconvexity posts a great challenge for global optimization methods. In the presence of the challenge, a special class of nonconvex functions called generalized-convex functions are still widely available in many applications and neurodynamic approaches to generalized-convex optimization is viable. In addition to the problems with generalized convexity, multiple-objective optimization is another interesting and important issue. Because of the multiplefacet nature of reality, multiple-objective optimization is more realistic and practical. While population-based evolutionary approaches to nonconvex and multiple-objective optimization emerged as prevailing heuristic and stochastic methods in recent years, neurodynamic approaches deserve in-depth investigations in their own rights due to their close ties with optimization and dynamical systems theories, as well as their biological plausibility and circuit implementability. In this proposed research, we will develop neurodynamic approaches to constrained optimization in the presence of generalized convexity and multiplicity in objective functions. The research will consist of three coherent parts. In the first part, we will begin with designing neurodynamic models for constrained optimization with generalized-convex functions based on our newly developed neurodynamic models for pseudo-convex optimization. Since many generalized convex functions have convexity-like global properties, it is highly possible to expand existing results for pseudo-convex optimization to cover more generalizedconvex problems. In the second part, we will focus on designing and analyzing neurodynamic models for multiple-objective optimization by means of adaptive scalarization. Finally, in the third part, the new results will be applied for intelligent control and dynamic portfolio optimization. It is expected that the accomplishments of the proposed project will significantly advance the frontiers of neurodynamic optimization research from both theoretical and practical points of view.