ABSTRACT
This paper surveys the state-of-the-art in continuous nonlinear optimization and makes the case that due to tremendous recent progress, larger and more complex problems can be solved than previously thought possible. The two basic paradigms, trust-region and line-search methods, are briefly described. In addition, various nonlinear optimization techniques are reviewed. The application of these nonlinear optimization methods to circuit sizing is presented by describing a pair of circuit sizing tools, one for dynamic tuning and one for tuning based on static timing analysis. Particular emphasis has been given to the customization of nonlinear optimization to the circuit sizing application.
- 1.R. G. Carter. On the global convergence of trust-region methods using inexact gradient information. SIAM Journal on Numerical Analysis, 28(1):251-265, 1991. Google ScholarDigital Library
- 2.C.-P. Chen, C. C. N. Chu, and D. F. Wong. Fast and exact simultaneous gate and wire sizing by Lagrangian Relaxation. IEEE International Conference on Computer-Aided Design, pages 617-624, November 1998. Google ScholarDigital Library
- 3.C.-P. Chen, C. N. Chu, and D. F. Wong. Fast and exact simultaneous gate and wire sizing by Lagrangian Relaxation. IEEE Transactions on Computer-Aided Design of ICs and Systems, 18(7), July 1999. Google ScholarDigital Library
- 4.A. R. Conn, P. K. Coulman, R. A. Haring, G. L. Morrill, and C. Visweswariah. Optimization of custom MOS circuits by transistor sizing. IEEE International Conference on Computer-Aided Design, pages 174-180, November 1996. Google ScholarDigital Library
- 5.A. R. Conn, P. K. Coulman, R. A. Haring, G. L. Morrill, C. Visweswariah, and C. W. Wu. JiffyTune: circuit optimization using time-domain sensitivities. IEEE Transactions on Computer-Aided Design of ICs and Systems, 17(12):1292-1309, December 1998. Google ScholarDigital Library
- 6.A. R. Conn, I. M. Elfadel, W. W. Molzen, Jr., P. R. O'Brien, P. N. Strenski, C. Visweswariah, and C. B. Whan. Gradient-based optimization of custom circuits using a static-timing formulation. Proc. 1999 Design Automation Conference, pages 452-459, June 1999. Google ScholarDigital Library
- 7.A. R. Conn, N. I. M. Gould, D. Orban, and Ph. L. Toint. A primal-dual trust-region algorithm for minimizing a nonconvex function subject to bound and linear equality constraints. Mathematical Programming, Series B, 87(2):215-249, 2000.Google ScholarCross Ref
- 8.A. R. Conn, N. I. M. Gould, A. Sartenaer, and Ph. L. Toint. Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints. SIAM Journal on Optimization, 3(1):164-221, 1993.Google ScholarCross Ref
- 9.A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM Journal on Numerical Analysis, 25:433-460, 1988. See also same journal, 26:764-767, 1989. Google ScholarDigital Library
- 10.A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Convergence of quasi-Newton matrices generated by the symmetric rank one update. Mathematical Programming, 50(2):177-196, 1991. Google ScholarDigital Library
- 11.A. R. Conn, N. I. M. Gould, and Ph. L. Toint. LANCELOT : a Fortran package for large-scale nonlinear optimization (Release A), volume 17 of Springer Series in Computational Mathematics. Springer Verlag, Heidelberg, Berlin, New York, 1992. Google ScholarDigital Library
- 12.A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Trust-Region Methods, volume 1 of MPS/SIAM Series on Optimization. SIAM and MPS, Philadelphia, USA, 2000. Google ScholarDigital Library
- 13.A. R. Conn, R. A. Haring, and C. Visweswariah. Noise considerations in circuit optimization. IEEE International Conference on Computer-Aided Design, pages 220-227, November 1998. Google ScholarDigital Library
- 14.A. R. Conn, R. A. Haring, C. Visweswariah, and C. W. Wu. Circuit optimization via adjoint Lagrangians. IEEE International Conference on Computer-Aided Design, pages 281-288, November 1997. Google ScholarDigital Library
- 15.A. R. Conn, K. Scheinberg, and Ph. L. Toint. Recent progress in unconstrained nonlinear optimization without derivatives. Mathematical Programming, Series B, 79(3):397-414, 1997. Google ScholarDigital Library
- 16.A. R. Conn, L. N. Vicente, and C. Visweswariah. Two-step algorithms for nonlinear optimization with structured applications. SIAM Journal on Optimization, 9(4):924-947, September 1999. Google ScholarDigital Library
- 17.P. Feldmann, T. V. Nguyen, S. W. Director, and R. A. Rohrer. Sensitivity computation in piecewise approximate circuit simulation. IEEE Transactions on Computer-Aided Design of ICs and Systems, 10(2):171--183, February 1991.Google ScholarDigital Library
- 18.A. V. Fiacco and G. P. McCormick. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. J. Wiley and Sons, New York, 1968. Reprinted as Classics in Applied Mathematics 4, SIAM, 1990.Google Scholar
- 19.R. Fletcher. Practical Methods of Optimization: Unconstrained Optimization. J. Wiley and Sons, New York, 1980. Google ScholarDigital Library
- 20.R. Fletcher, N. I. M. Gould, S. Leyer, and Ph. L. Toint. Global convergence of trust-region SQP-filter algorithms for nonlinear programming. Technical Report 99/03, Department of Mathematics, FUNDP, Namur, Belgium, 1999.Google Scholar
- 21.R. Fletcher and S. Leyer. Nonlinear programming without a penalty function. Technical Report Technical Report NA/171, Department of Mathematics, University of Dundee, Dundee, UK, 1997.Google Scholar
- 22.P. E. Gill, W. Murray, and M. A. Saunders. SNOPT 5.3 USER'S GUIDE. Technical Report NA97-5, Department of Mathematics, University of California, San Diego, USA, 1997.Google Scholar
- 23.N. I. M. Gould and Ph. L. Toint. Modern methods for non-convex quadratic programming. Technical Report RAL-TR-2001-009, Rutherford Appleton Laboratory, Chilton, Oxfordshire, England, 2001.Google Scholar
- 24.A. Griewank. On automatic differentiation. In M. Iri and K. Tanabe, editors, Mathematical Programming: recent developments and applications, pages 83-108. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.Google Scholar
- 25.A. Griewank and Ph. L. Toint. On the unconstrained optimization of partially separable functions. In M. J. D. Powell, editor, Nonlinear Optimization 1981, pages 301-312. Academic Press, London and New York, 1982.Google Scholar
- 26.B. A. Murtagh and M. A. Saunders. MINOS 5.4 USER'S GUIDE (revised). Technical Report SOL 83-20R, Department of Operations Research, Stanford University, Stanford, CA 94305, USA, 1993. Revised 1995.Google Scholar
- 27.S. G. Nash and A. Sofer. Linear and nonlinear programming. Prentice-Hall, Englewood Cliffs, NJ, 1996.Google Scholar
- 28.J. A. Nelder and R. Mead. A simplex method for function minimization. Computer Journal, 7:308-313, 1965.Google ScholarCross Ref
- 29.J. Nocedal and S. J. Wright. Numerical Optimization. Springer Verlag, Heidelberg, Berlin, New York, 1999.Google Scholar
- 30.G. A. Northrop and P.-F. Lu. A semi-custom design ow in high-performance microprocessor design. Proc. 2001 Design Automation Conference, June 2001. To be published. Google ScholarDigital Library
- 31.V. B. Rao, J. P. Soreff, T. B. Brodnax, and R. E. Mains. EinsTLT: transistor level timing with EinsTimer. Proc. TAU, December 1999.Google Scholar
- 32.A. Srinivasan, K. Chaudhary, and E. S. Kuh. RITUAL: A performance driven placement algorithm for small cell ICs. IEEE International Conference on Computer-Aided Design, pages 48-51, November 1991.Google ScholarCross Ref
- 33.R. J. Vanderbei. LOQO user's manual - version 3.10. Optimization Methods and Software, 12:485-514, 1999.Google ScholarCross Ref
- 34.C. Visweswariah. Formal static optimization of high-performance digital circuits. Proc. TAU, page 51, December 2000.Google Scholar
- 35.C. Visweswariah and A. R. Conn. Formulation of static circuit optimization with reduced size, degeneracy and redundancy by timing graph manipulation. IEEE International Conference on Computer-Aided Design, pages 244-251, November 1999. Google ScholarDigital Library
- 36.C. Visweswariah, R. A. Haring, and A. R. Conn. Noise considerations in circuit optimization. IEEE Transactions on Computer-Aided Design of ICs and Systems, 19(6):679-690, June 2000. Google ScholarDigital Library
- 37.C. Visweswariah and R. A. Rohrer. Piecewise approximate circuit simulation. IEEE Transactions on Computer-Aided Design of ICs and Systems, 10(7):861-870, July 1991.Google ScholarDigital Library
- 38.M. H. Wright. Interior methods for constrained optimization. In A. Iserles, editor, Acta Numerica, volume 1, pages 341-407. Cambridge Univesity Press, New York, 1992.Google Scholar
Index Terms
- Overview of continuous optimization advances and applications to circuit tuning
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