Applications of semidefinite programming
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Optimized power-delay curve generation for standard cell ICs
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Gate sizing using Lagrangian relaxation combined with a fast gradient-based pre-processing step
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Convex Optimization
Gate sizing for crosstalk reduction under timing constraints by Lagrangian relaxation
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Variability driven gate sizing for binning yield optimization
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient design space exploration for component-based system design
Proceedings of the International Conference on Computer-Aided Design
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Convex optimization problems are very popular in the VLSI design society due to their guaranteed convergence to a global optimal point. Table data is often fitted into analytical forms like posynomials to make them convex. However, fitting the look-up tables into posynomial forms with minimum error itself may not be a convex optimization problem and hence excessive fitting errors may be introduced. In recent literature numerically convex tables have been proposed. These tables are created optimally by minimizing the perturbation of data to make them numerically convex. But since these tables are numerical, it is extremely important to make the table data smooth, and yet preserve its convexity. Smoothness will ensure that the convex optimizer behaves in a predictable way and converges quickly to the global optimal point. In this paper, we propose to simultaneously create optimal numerically convex look-up tables and guarantee smoothness in the data. We show that numerically "convexifying" and "smoothing" the table data with minimum perturbation can be formulated as a convex semidefinite optimization problem and hence optimality can be reached in polynomial time. We present our convexifying and smoothing results on industrial cell libraries. ConvexSmooth shows 14X reduction in fitting error over a well-developed posynomial fitting algorithm.