1. University of Washington, Industrial and Systems Engineering, Seattle, WA, United States;2. Citi Alternative Investments, New York, NY, United States;3. Webtrends, Seattle, WA, United States
Abstract:
We develop a chattering approach to solve variational problems that lack traditional properties such as differentiable everywhere and convexity conditions. We prove that our chattering approximation approaches the true relaxed solution as the intervals get smaller. Our chattering approach suggests a nonlinear optimization problem that can be easily solved to recover the optimal trajectory. A numerical example demonstrates our approach.