Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Global convergence of a class of trust region algorithms for optimization with simple bounds
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Incremental event-driven simulation of digital FET circuits
DAC '93 Proceedings of the 30th international Design Automation Conference
A sequential quadratic programming approach to concurrent gate and wire sizing
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Power vs. delay in gate sizing: conflicting objectives?
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Optimization of custom MOS circuits by transistor sizing
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Sensitivity and Optimization
Optimal design of macrocells for low power and high speed
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Optimization techniques for high-performance digital circuits
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Noise considerations in circuit optimization
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Gradient-based optimization of custom circuits using a static-timing formulation
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Overview of continuous optimization advances and applications to circuit tuning
Proceedings of the 2001 international symposium on Physical design
Hybrid structured clock network construction
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
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The circuit tuning problem is best approached by means of gradient-based nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable parameters, the direct method is used to repeatedly solve the associated sensitivity circuit to obtain all the necessary gradients. Likewise, when the parameters outnumber the measurements, the adjoint method is employed to solve the adjoint circuit repeatedly for each measurement to compute the sensitivities. In this paper, we propose the adjoint Lagrangian method, which computes all the gradients necessary for augmented-Lagrangian-based optimization in a single adjoint analysis. After the nominal simulation of the circuit has been carried out, the gradients of the merit function are expressed as the gradients of a weighted sum of circuit measurements. The weights are dependent on the nominal solution and on optimizer quantities such as Lagrange multipliers. By suitably choosing the excitations of the adjoint circuit, the gradients of the merit function are computed via a single adjoint analysis, irrespective of the number of measurements and the number of parameters of the optimization. This procedure requires close integration between the nonlinear optimization software and the circuit simulation program. The adjoint Lagrangian formulation has been implemented in the JiffyTune tool which optimizes delay, area, slew (transition time) and power measurements by adjusting transistor widths and wire sizes. Speedups of over 35x have been realized in the gradient computation procedure by using the adjoint Lagrangian formulation, leading to speedups of up to 2.5x in the overall optimization procedure. Perhaps more importantly, these speedups have rendered feasible the tuning of large circuits. A circuit with 6,900 transistors was optimized in under two hours of CPU time.