A survey of optimization techniques for integrated-circuit design

We survey contemporary optimization techniques and relate these to optimization problems which arise in the design of integrated circuits. Theory, algorithms and programs are reviewed, and an assessment is made of the impact optimization has had and will have on integrated-circuit design. Integrated circuits are characterized by complex tradeoffs between multiple nonlinear objectives with multiple nonlinear and sometimes nonconvex constraints. Function and gradient evaluations require the solution of very large sets of nonlinear differential equations, consequently they are inaccurate and extremely expensive. Furthermore, the partmeters to be optimized are subject to inherent statistical fluctuations. We focus on those multiobjective constrained optimization techniques which are appropriate to this environment.

[1]  L. Armijo Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[2]  G. D. Hachtel,et al.  Techniques for the optimal design and synthesis of switching circuits , 1967 .

[3]  Donald R. Chand,et al.  An Algorithm for Convex Polytopes , 1970, JACM.

[4]  B. Eaves,et al.  Generalized Cutting Plane Algorithms , 1971 .

[5]  Robert K. Brayton,et al.  The Sparse Tableau Approach to Network Analysis and Design , 1971 .

[6]  J. F. Pinel,et al.  Tolerance assignment in linear networks using nonlinear programming , 1972 .

[7]  E. Polak,et al.  Rate of Convergence of a Class of Methods of Feasible Directions , 1973 .

[8]  C. Charalambous,et al.  New Algorithms for Network Optimization , 1973 .

[9]  K.-H. Leung,et al.  Tracking sensitivity: an efficient algorithm for linear nonreciprocal circuits , 1974 .

[10]  K.-H. Leung,et al.  Efficient statistical circuit analysis , 1974 .

[11]  K. Madsen,et al.  Automated minimax design of networks , 1975 .

[12]  K. Madsen An Algorithm for Minimax Solution of Overdetermined Systems of Non-linear Equations , 1975 .

[13]  John W. Bandler,et al.  Worst Case Network Tolerance Optimization , 1975 .

[14]  Hans Schjær-Jacobsen,et al.  Efficient Minimax Design of Networks without Using Derivatives , 1975 .

[15]  Shih-Ping Han,et al.  Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[16]  K. Madsen,et al.  Singularities in minimax optimization of networks , 1976 .

[17]  Dimitri P. Bertsekas,et al.  Multiplier methods: A survey , 1975, at - Automatisierungstechnik.

[18]  T. Scott,et al.  Regionalization: A method for generating joint density estimates , 1976 .

[19]  G. Hachtel The simplicial approximation approach to design centering , 1977 .

[20]  T. Neumann,et al.  Tracking sensitivity: a practical algorithm , 1977 .

[21]  Niklaus Wirth,et al.  Modula: A language for modular multiprogramming , 1977, Softw. Pract. Exp..

[22]  Y. Censor Pareto optimality in multiobjective problems , 1977 .

[23]  A. Hoffman,et al.  A theorem on inverses of convex sets of real matrices with application to the worst case dc problem , 1977 .

[24]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[25]  D. Mayne,et al.  An outer approximations algorithm for computer-aided design problems , 1979 .

[26]  E. Polak,et al.  Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem , 1979 .

[27]  Robert K. Brayton,et al.  A new algorithm for statistical circuit design based on quasi-newton methods and function splitting , 1979 .

[28]  C. C. Gonzaga,et al.  On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms , 1979 .

[29]  John W. Bandler,et al.  Optimization of electrical circuits , 1979 .

[30]  K. Madsen,et al.  Algorithms for worst-case tolerance optimization , 1979 .

[31]  David Q. Mayne,et al.  Combined phase I—phase II methods of feasible directions , 1979, Math. Program..

[32]  K. S. Tahim,et al.  A radial exploration approach to manufacturing yield estimation and design centering , 1979 .

[33]  Elijah Polak,et al.  Algorithms for a class of computer-aided design problems: A review , 1979, Autom..

[34]  R. Brayton,et al.  Yield maximization and worst-case design with arbitrary statistical distributions , 1980 .

[35]  C. C. Gonzaga,et al.  An improved algorithm for optimization problems with functional inequality constraints , 1980 .

[36]  Jerker Wilander An interactive programming system for Pascal , 1980, BIT Comput. Sci. Sect..

[37]  T. Scott,et al.  An interactive linear programming approach to model parameter fitting and worst case circuit design , 1980 .

[38]  Stephen W. Director,et al.  Comparison of two methods for design centering , 1981 .

[39]  K. Singhal,et al.  Statistical design centering and tolerancing using parametric sampling , 1981 .

[40]  Kaj Madsen,et al.  Combined lp and quasi-Newton methods for minimax optimization , 1981, Math. Program..

[41]  André L. Tits,et al.  The design of digital filters using interactive optimization , 1981, CDC 1981.

[42]  E. Polak,et al.  A recursive quadratic programming algorithm for semi-infinite optimization problems , 1982 .

[43]  E. Polak An implementable algorithm for the optimal design centering, tolerancing, and tuning problem , 1982 .