Nesterov’s Smoothing and Excessive Gap Methods for an Optimization Problem in VLSI Placement

Abstract

In this paper, we propose an algorithm for a nonsmooth convex optimization problem arising in very large-scale integrated circuit placement. The objective function is the sum of a large number of Half-Perimeter Wire Length (HPWL) functions and a strongly convex function. The algorithm is based on Nesterov’s smoothing and excessive gap techniques. The main advantage of the algorithm is that it can capture the HPWL information in the process of optimization, and every subproblem has an explicit solution in the process of optimization. The convergence rate of the algorithm is $$O(1/k^{2}),$$ where k is the iteration counter, which is optimal. We also present preliminary experiments on nine placement contest benchmarks. Numerical examples confirm the theoretical results.