  We consider a smoothed online convex optimization (SOCO) problem with
predictions, where the learner has access to a finite lookahead window of
time-varying stage costs, but suffers a switching cost for changing its actions
at each stage. Based on the Alternating Proximal Gradient Descent (APGD)
framework, we develop Receding Horizon Alternating Proximal Descent (RHAPD) for
proximable, non-smooth and strongly convex stage costs, and RHAPD-Smooth
(RHAPD-S) for non-proximable, smooth and strongly convex stage costs. In
addition to outperforming gradient descent-based algorithms, while maintaining
a comparable runtime complexity, our proposed algorithms also allow us to solve
a wider range of problems. We provide theoretical upper bounds on the dynamic
regret achieved by the proposed algorithms, which decay exponentially with the
length of the lookahead window. The performance of the presented algorithms is
empirically demonstrated via numerical experiments on non-smooth regression,
dynamic trajectory tracking, and {economic power dispatch} problems.
