Reference:
M. Gerard,
B. De Schutter, and
M. Verhaegen,
"A hybrid steepest descent method for constrained convex
optimization," Automatica, vol. 45, no. 2, pp. 525-531, Feb.
2009.
Abstract:
This paper describes a hybrid steepest descent method to decrease over
time any given convex cost function while keeping the optimization
variables into any given convex set. The method takes advantage of
properties of hybrid systems to avoid the computation of projections
or of a dual optimum. The convergence to a global optimum is analyzed
using Lyapunov stability arguments. A discretized implementation and
simulation results are presented and analyzed. This method is of
practical interest to integrate real-time convex optimization into
embedded controllers thanks to its implementation as a dynamical
system, its simplicity, and its low computation cost.