Advancement: Hybrid Methods for Optimization with High Performance and Robustness

Speaker Name: 
Dawn Hustig-Schultz
Speaker Title: 
PhD Student (Advisor: Ricardo Sanfelice)
Speaker Organization: 
Computer Engineering
Start Time: 
Friday, November 30, 2018 - 12:30pm
End Time: 
Friday, November 30, 2018 - 2:30pm
Location: 
Engineering 2, Room 280
Organizer: 
Ricardo Sanfelice

Abstract:  Optimization has valuable applications in many areas of technology, including smart grids, multiagent systems, wireless sensor and communications networks, and deep learning. This research aims to develop hybrid algorithms for global optimization with fast convergence, stability, and robustness. Two algorithms have been developed: one yielding increased performance and one ensuring global convergence.

The algorithm for increased performance features a uniting control strategy, in which two standard heavy ball algorithms, one used globally and another used locally, with properly designed gravity and friction parameters, are employed. This hybrid control strategy switches the parameters to converge quickly to the set of minimizers of the convex optimization function without oscillations. A hybrid control algorithm implementing a switching strategy that measures the objective function and its gradient, and another algorithm that only measures its gradient, are designed. The hybrid algorithm for global convergence of Morse objective functions, which have isolated maxima and minima, uses hysteresis to determine when the system starts at a local maximum of a nonconvex objective function, and then increases the “velocity” term of the heavy ball algorithm to move the system away from this maximum to converge to a local minimum.

Key properties of the resulting closed-loop systems, including existence of solutions, asymptotic stability, and robustness are analyzed. The ongoing work for both algorithms is illustrated by numerical examples. Future research will focus on a general hybrid optimization framework which combines increased performance and global convergence, with applications for multiagent systems.