We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (op-amps). 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 trade-o s among competing performance measures such aspower, open-loop 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 trade-o curves relating performance measures such as power dissipation, unity-gain bandwidth, and open-loop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the speci cations for a

Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interior-point type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems that also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for large-scale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Department of Management, Odense University, Campusvej 55, DK-5230 Odense M, Denmark. E-mail: eda@busieco.ou.dk y ...

In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a path-based delay model to capture the timing constraints in the circuit. To reduce the problem size and improve the solution convergence, we iteratively identify and optimize the kmost critical paths in the circuit and their neighboring cells. More precisely in each iteration, we perform three operations: a) reposition the immediate fan-outs of the gates on the k-most critical paths; b) size down the immediate fan-outs of the gates on the k-most critical paths; c) simultaneously reposition and resize the gates on the k-most critical paths. Each of these operations is formulated and solved as a mathematical program by using efficient solution techniques. Experimental results on a set of benchmark circuits demonstrate the effectiveness of our approach compared to the conventional approaches which separate gate sizing from gate placement. 1

Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schur-concave functions, which are the class of functions consistent with the so-called Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schur-concave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.

We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and non-convex constraints. Adding a limited set of non-convex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and IDS. To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18 µm technology for varying speed requirements and is compared with simulations and designs obtained from geometric programming. Categories and Subject Descriptors:

This paper develops a simple bounding procedure for the optimal value of a posynomial geometric programming (GP) problem when some of the coefficients for terms in the problem's objective function are estimated with error. The bound may be computed even before the problem is solved and it is shown analytically that the optimum value is very insensitive to errors in the coefficients; for example, a 20% error could cause the optimum to be wrong by no more than 1.67%. Key Words: Geometric Programming, Posynomials, Sensitivity Analysis *Corresponding Author Address: Department of Industrial Engineering 1048 Benedum Hall University of Pittsburgh Pittsburgh, PA 15261 e-mail: rajgopal@engrng.pitt.edu fax: (412) 624-9831 1 Introduction Geometric Programming (GP) is a technique for solving certain classes of algebraic nonlinear optimization problems. Since its original development by Duffin, Peterson and Zener (1967) at the Westinghouse R & D Center, it has been studied extensively and...

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 two-stage 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...

Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addressed through the use of decomposition-based methods, several of which have recently been developed. Two of these methods are collaborative optimization (CO) and analytical target cascading (ATC). CO was conceived in 1994 in response to multidisciplinary design needs in the aerospace industry. Recent progress has led to an updated version, enhanced collaborative optimization (ECO), that is introduced in this paper. ECO addresses many of the computational challenges inherent in CO, yielding significant computational savings and more robust solutions. ATC was formalized in 2000 to address needs in the automotive industry. While ATC was originally developed for object-based decomposition, it is also applicable to multidisciplinary design problems. In this paper, both methods are applied to a set of test cases. The goal is to introduce the ECO methodology by comparing and contrasting it with ATC, a method familiar within the mechanical engineering design community. Comparison of ECO and ATC is not intended to establish the computational superiority of either method. Rather, these two methods are compared as a means of highlighting several promising approaches to the coordination of distributed design problems.

We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and non-convex constraints. Adding a limited set of non-convex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and Ips. To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18'pm technology for varying speed requirements and is compared with simnlations and designs obtained from geometric programming. Categories and Subject Descriptors:

Abstract not found