Tractable approximate robust geometric programming

Hsiung, Kan-Lin; Kim, Seung-Jean; Boyd, Stephen

doi:10.1007/s11081-007-9025-z

Cited by 41 publications

(17 citation statements)

References 50 publications

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“…Reformulations of polynomial [34,57,73,93] and posynomial [75,95] programs also attracted considerable attention. Most work in geometric programming rests on a convex reformulation [40]; a symbolic method to model problems so that the corresponding mathematical program is convex is described in [30]. Reformulations are used within algorithms [65], specially in decomposition-based ones [7].…”

Section: Reformulationsmentioning

confidence: 99%

Reformulations in Mathematical Programming: Definitions and Systematics

Liberti

2009

RAIRO-Oper. Res.

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Abstract. A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are very common in mathematical programming but interestingly they have never been studied under a common framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations, give several fundamental definitions categorizing reformulations in essentially four types (opt-reformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type. Keywords

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Section: Reformulationsmentioning

confidence: 99%

Reformulations in Mathematical Programming: Definitions and Systematics

Liberti

2009

RAIRO-Oper. Res.

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“…Using duality techniques from convex optimization, we reformulate these constraints in a tractably solvable fashion (see [7], [2] for details).…”

Section: Exploiting Modeling Error Statistics To Drive Optimizatimentioning

confidence: 99%

An algorithm for exploiting modeling error statistics to enable robust analog optimization

Singh¹,

Lok²,

Ragab³

et al. 2010

2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Abstract-Equation-based optimization using geometric programming (GP) for automated synthesis of analog circuits has recently gained broader adoption. A major outstanding challenge is the inaccuracy resulting from fitting the complex behavior of scaled transistors to posynomial functions. Fitting over a large region can be grossly inaccurate, and in fact, poor posynomial fit can lead to failure to find a true feasible solution. On the other hand, fitting over smaller regions and then selecting the best region, incurs exponential complexity.In this paper, we advance a novel optimization strategy that circumvents these dueling problems in the following manner: by explicitly handling the error of the model in the course of optimization, we find a potentially suboptimal, but feasible solution. This solution subsequently guides a range-refinement process of our transistor models, allowing us to reduce the range of operating conditions and dimensions, and hence obtain far more accurate GP models.The key contribution is in using the available oracle (SPICE simulations) to identify solutions that are feasible with respect to the accurate behavior rather than the fitted model. The key innovation is the explicit link between the fitting error statistics and the rate of the error uncertainty set increase, which we use in a robust optimization formulation to find feasible solutions.We demonstrate the effectiveness of our algorithm on a two benchmarks: a two-stage CMOS operational amplifier and a voltage controlled oscillator designed in TSMC 0.18µm CMOS technology. Our algorithm is able to identify superior solution points producing uniformly better power and area values under gain constraint with improvements of up to 50% in power and 10% in area for the amplifier design. We also demonstrate that when utilizing the models with the same level of modeling error, our method yields solutions that meet the constraints while the violations for the standard method were as high as 45% and larger than 15% for several constraints.

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“…However, a tractable approximation method that yields a good compromise between solution accuracy and computational efficiency has been proposed. Refer to [20] for more details.…”

Section: B Robust Optimization With Ellipsoidal Uncertaintymentioning

confidence: 99%

“…We further use the concentric ellipsoids E γ (20) with various values of γ to capture different degrees of process variations. The tradeoff between the design cost and the yield bound is shown in Fig.…”

Section: ) Robust Optimization Of An Romentioning

confidence: 99%

See 1 more Smart Citation

Regular Analog/RF Integrated Circuits Design Using Optimization With Recourse Including Ellipsoidal Uncertainty

Hsiung

et al. 2009

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-Long design cycles due to the inability to predict silicon realities are a well-known problem that plagues analog/RF integrated circuit product development. As this problem worsens for nanoscale IC technologies, the high cost of design and multiple manufacturing spins causes fewer products to have the volume required to support full-custom implementation. Design reuse and analog synthesis make analog/RF design more affordable; however, the increasing process variability and lack of modeling accuracy remain extremely challenging for nanoscale analog/RF design. We propose a regular analog/RF IC using metal-mask configurability design methodology Optimization with Recourse of Analog Circuits including Layout Extraction (ORACLE), which is a combination of reuse and shared-use by formulating the synthesis problem as an optimization with recourse problem. Using a two-stage geometric programming with recourse approach, ORACLE solves for both the globally optimal shared and application-specific variables. Furthermore, robust optimization is proposed to treat the design with variability problem, further enhancing the ORACLE methodology by providing yield bound for each configuration of regular designs. The statistical variations of the process parameters are captured by a confidence ellipsoid. We demonstrate ORACLE for regular Low Noise Amplifier designs using metal-mask configurability, where a range of applications share common underlying structure and application-specific customization is performed using the metal-mask layers. Two RF oscillator design examples are shown to achieve robust designs with guaranteed yield bound.

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Tractable approximate robust geometric programming

Cited by 41 publications

References 50 publications

Reformulations in Mathematical Programming: Definitions and Systematics

Reformulations in Mathematical Programming: Definitions and Systematics

An algorithm for exploiting modeling error statistics to enable robust analog optimization

Regular Analog/RF Integrated Circuits Design Using Optimization With Recourse Including Ellipsoidal Uncertainty

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