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

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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

Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these optimization problems. However, there are few convergence guarantees for such algorithms, and the algorithms are therefore not guaranteed to solve the corresponding optimization problem. Here we present an oriented tree decomposition algorithm that is guaranteed to converge to the global optimum of the Tree-Reweighted (TRW) variational problem. Our algorithm performs local updates in the convex dual of the TRW problem – an unconstrained generalized geometric program. Primal updates, also local, correspond to oriented reparametrization operations that leave the distribution intact. 1

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In the recent past a number of papers were written that present low complexity interior-point methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is self-concordant, and that the analyses of interiorpoint methods for these programs can thus be reduced to the analysis of interior-point methods with self-concordant barrier functions. Key words: interior-point method, barrier function, dual geometric programming, (extended) entropy programming, primal and dual l p -programming, relative Lipschitz condition, scaled Lipschitz condition, self-concordance. 1 Introduction The efficiency of a barrier method for solving convex programs strongly depends on the properties of the barrier function used. A key property that is sufficient to prove fast convergence for barrier methods is the property of self-concordance introduced in [17]. This condition not only allows a proof of polynomial convergen...

A genetic algorithm (GA) is a search and optimization method developed by mimicking the evolutionary principles and chromosomal processing in natural genetics. A GA begins its search with a random set of solutions usually coded in binary string structures. Every solution is assigned a fitness which is directly related to the objective function of the search and optimization problem. Thereafter, the population of solutions is modified to a new population by applying three operators similar to natural genetic operators---reproduction, crossover, and mutation. A GA works iteratively by successively applying these three operators in each generation till a termination criterion is satisfied. Over the past one decade, GAs have been successfully applied to a wide variety of problems, because of their simplicity, global perspective, and inherent parallel processing. In this paper, we outline the working principle of a GA by describing these three operators and by outlining an intuitive sketch ...

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The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express the forward rates zk(tk − t0) = � k−1 i=0 fi,i+1(ti+1 − ti), where xi,i+1 = e −fi,i+1 in Tables 2–4. Note that the are n equations in m unknowns (n = m =5). Ordinary bootstrapping does not work when n � = m, eg., if there were no 0.5 time T–Bill. 1 (1)