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Optimal design of a CMOS opamp via geometric programming
 IEEE Transactions on ComputerAided Design
, 2001
"... We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er ..."
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Cited by 51 (10 self)
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We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er design problem can be expressed as a special form of optimization problem called geometric programming, for which very e cient global optimization methods have been developed. As a consequence we can e ciently determine globally optimal ampli er designs, or globally optimal tradeo s among competing performance measures such aspower, openloop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS ampli ers, directly from speci cations. In this paper we apply this method to a speci c, widely used operational ampli er architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal tradeo curves relating performance measures such as power dissipation, unitygain bandwidth, and openloop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the speci cations for a
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
"... ..."
Concurrent Logic Restructuring and Placement for Timing Closure
 in Proc. IEEE International Conference on Computer Aided Design
, 1999
"... ABSTRACT: In this paper, an algorithm for simultaneous logic restructuring and placement is presented. This algorithm first constructs a set of supercells along the critical paths and then generates the set of noninferior remapping solutions for each supercell. The best mapping and placement solu ..."
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Cited by 13 (0 self)
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ABSTRACT: In this paper, an algorithm for simultaneous logic restructuring and placement is presented. This algorithm first constructs a set of supercells along the critical paths and then generates the set of noninferior remapping solutions for each supercell. The best mapping and placement solutions for all supercells are obtained by solving a generalized geometric programming (GGP) problem. The process of identifying and optimizing the critical paths is iterated until timing closure is achieved. Experimental results on a set of MCNC benchmarks demonstrate the effectiveness of our algorithm. I.
Global Optimization in Generalized Geometric Programming
 Engng
, 1997
"... A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP). By utilizing an exponential variable transformation the initial nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints ..."
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Cited by 12 (3 self)
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A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP). By utilizing an exponential variable transformation the initial nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints and the objective are decomposed into the difference of two convex functions. A convex relaxation of problem (DC) is then obtained based on the linear lower bounding of the concave parts of the objective function and constraints inside some box region. The proposed branch and bound type algorithm attains finite fflconvergence to the global minimum through the successive refinement of a convex relaxation of the feasible region and/or of the objective function and the subsequent solution of a series of nonlinear convex optimization problems. The efficiency of the proposed approach is enhanced by eliminating variables through monotonicity analysis, by maintaining tightly bound variables thro...
LARGE SCALE GEOMETRIC PROGRAMMING: AN APPLICATION IN CODING THEORY
"... Geometric programming is an optimization technique originally developed for solving a class of nonlinear optimization problems found in engineering and design. Previous applications have generally been small scale and highly nonlinear. In a geometric programming problem all the constraints as well a ..."
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Cited by 1 (0 self)
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Geometric programming is an optimization technique originally developed for solving a class of nonlinear optimization problems found in engineering and design. Previous applications have generally been small scale and highly nonlinear. In a geometric programming problem all the constraints as well as the objective function are posynomials. The Gaussian channel is a communications model in which messages are represented by vectors in R n. The transmitter has a finite set of messages available and these messages are transmitted over a noisy channel to a receiver. The received message equals the sent vector perturbed by a Gaussian noise vector. The receiver must decide which of the messages was sent. We use groups of orthogonal matrices to generate the message set and the result is called a group code. The problem of finding the best code generated by a particular group is called the initial vector problem. Previous attempts to find a general solution to this problem have been unsuccessful. Although, it has been solved in several special cases. We write this problem as a nonlinear programming problem,
Modular Test Plans for Certification of Software Reliability
"... This paper considers the problem of certifying the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities ..."
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This paper considers the problem of certifying the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities. A test procedure is considered in which only the individual modules are tested and the system is certified if, and only if, no failures are observed. The minimum number of tests required of each module is determined such that the probability of certifying a system whose reliability falls below a specified value R 0 is less than a specified small fraction b. This sample size determination problem is formulated as a twostage mathematical program and an algorithm is developed for solving this problem. Two examples from the literature are considered to demonstrate the procedure. Keywords: Software reliability; Modular Tests; Sample Size Determination; Mathematical Programming 1 1. Introduc...