Digital Circuit Optimization via Geometric Programming

Boyd, Stephen; Kim, Seung-Jean; Patil, Dinesh; Horowitz, Mark

doi:10.1287/opre.1050.0254

Cited by 151 publications

(149 citation statements)

References 154 publications

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“…It has been shown that geometric programming (GP) can be solved efficiently and reliably by many methods, even for large-scale problems, and GP has been used widely in engineering for resource allocation in communication and network systems, inventory control, and other applications (34)(35)(36). For more information on the GP and its extensions and applications, some useful studies can be found elsewhere (37)(38)(39)(40)(41)(42).…”

Section: Generalized Geometric Programmingmentioning

confidence: 99%

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Wang²

2016

Transportation Research Record

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To satisfy growing travel demand and reduce traffic congestion, the continuous network design problem (CNDP) is often proposed to optimize road network performance by the expansion of road capacity. In the determination of the equilibrium travel flow pattern, equilibrium principles such as deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) may be applied to describe travelers’ route choice behavior. Because of the different mathematical formulation structures for the CNDP with DUE and SUE principles, most of the existing solution algorithms have been developed to solve the CNDP for either DUE or SUE. In this study, a more general solution method is proposed by applying the generalized geometric programming (GGP) approach to obtain the global optimal solution of the CNDP with both DUE and SUE principles. Specifically, the original CNDP problem is reformulated into a GGP form, and then a successive monomial approximation method is employed to transform the GGP formulation into a standard geometric programming form, which can be cast into an equivalent nonlinear but convex optimization problem whose global optimal solution can be guaranteed and solved by many existing solution algorithms. Numerical experiments are presented to demonstrate the validity and efficiency of the solution method.

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Section: Generalized Geometric Programmingmentioning

confidence: 99%

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Wang²

2016

Transportation Research Record

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“…Despite significant work on early applications in structural design [28], network flow [29], and optimal control [30,31], reliable and efficient numerical methods for solving GPs were not available until the 1990's [32]. GP has recently undergone a resurgence as researchers discover promising applications in digital circuit design [24], communication systems [25], antenna optimization [26], and statistics [23].…”

Section: Geometric Programmingmentioning

confidence: 99%

“…Like solving least-squares problems or linear programs a , solving standard classes of convex optimization problems exactly is a straightforward task for modern solvers. Recently, an increasing number of engineering disciplines have begun utilizing and relying upon this new technology [24][25][26]. That said, convex optimization is notably absent from most MDO approaches, with the exception of sequential quadratic programming (SQP) methods for solving nonconvex optimization problems locally.…”

Section: Introductionmentioning

confidence: 99%

Geometric Programming for Aircraft Design Optimization

Hoburg

Abbeel

2014

AIAA Journal

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We propose formulating conceptual-stage aircraft design problems as geometric programs (GPs), which are a specific type of convex optimization problem. Recent advances in convex optimization offer significant advantages over the general nonlinear optimization methods typically used in aircraft design. Modern GP solvers are extremely fast, even on large problems, require no initial guesses or tuning of solver parameters, and guarantee globally optimal solutions. These benefits come at a price: all objective and constraint functions -the mathematical models that describe aircraft design relations -must be expressed within the restricted functional forms of GP. Perhaps surprisingly, this restricted set of functional forms appears again and again in prevailing physics-based models for aircraft systems. Moreover, we show that for various models that cannot be manipulated algebraically into the forms required by GP, we can often fit compact GP models which accurately approximate the original models. The speed and reliability of GP solution methods makes them a promising approach for conceptual-stage aircraft design problems.

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“…Several methods can be used to achieve higher accuracy (if it is needed). First, our method can be extended to more complex (and accurate) models that account for differing rising and falling gate delays, the effects of signal slope, and better models of gate and wire load delay, as described in [3]. Another approach to obtaining higher accuracy is to use the method described in this paper to find an initial design, and then use a local optimization method, with accurate models, to fine-tune this design.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, we use a local method, with accurate timing models, to fine-tune the design. In this approach, the RC gate-sizing method described in this paper is used as a fast method for obtaining a good initial condition for a local optimization method (see, for example, [3]). …”

Section: Introductionmentioning

confidence: 99%

An Efficient Method for Large-Scale Gate Sizing

Joshi

Boyd

2008

IEEE Trans. Circuits Syst. I

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Abstract-We consider the problem of choosing the gate sizes or scale factors in a combinational logic circuit in order to minimize the total area, subject to simple RC timing constraints, and a minimum-allowed gate size. This problem is well known to be a geometric program (GP), and can be solved by using standard interiorpoint methods for small-and medium-size problems with up to several thousand gates. In this paper, we describe a new method for solving this problem that handles far larger circuits, up to a million gates, and is far faster. Numerical experiments show that our method can compute an adequately accurate solution within around 200 iterations; each iteration, in turn, consists of a few passes over the circuit. In particular, the complexity of our method, with a fixed number of iterations, is linear in the number of gates. A simple implementation of our algorithm can size a 10 000 gate circuit in 25 s, a 100 000 gate circuit in 4 min, and a million gate circuit in 40 min, approximately. For the million gate circuit, the associated GP has three million variables and more than six million monomial terms in its constraints; as far as we know, these are the largest GPs ever solved.

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Digital Circuit Optimization via Geometric Programming

Cited by 151 publications

References 154 publications

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Geometric Programming for Aircraft Design Optimization

An Efficient Method for Large-Scale Gate Sizing

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