On the convergence of the coordinate descent method for convex differentiable minimization
Journal of Optimization Theory and Applications
Greedy wire-sizing is linear time
ISPD '98 Proceedings of the 1998 international symposium on Physical design
Fast and exact simultaneous gate and wire sizing by Lagrangian relaxation
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
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
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The method of cyclic relaxation for the minimization of a function depending on several variables cyclically updates the value of each of the variables to its optimum subject to the condition that the remaining variables are fixed. We present a simple and transparent proof for the fact that cyclic relaxation converges linearly to an optimum solution when applied to the minimization of functions of the form $f(x_{1},\ldots,x_{n})=\sum_{i=1}^{n}\sum_{j=1}^{n}a_{i,j}\frac{x_{i}}{x_{j}}+\sum_{i=1}^{n}(b_{i}x_{i}+\frac{c_{i}}{x_{i}})$ for a i,j ,b i ,c i 驴驴驴0 with max驴{min驴{b 1,b 2,驴,b n },min驴{c 1,c 2,驴,c n }}0 over the n-dimensional interval [l 1,u 1]脳[l 2,u 2]脳驴驴驴脳[l n ,u n ] with 0l i u i for 1驴i驴n. Our result generalizes several convergence results that have been observed for algorithms applied to gate- and wire-sizing problems that arise in chip design.