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22
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 75 (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
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A Computational Study of the Homogeneous Algorithm for LargeScale Convex Optimization
, 1997
"... Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of th ..."
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Cited by 21 (1 self)
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Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint 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 largescale 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, DK5230 Odense M, Denmark. Email: eda@busieco.ou.dk y ...
Convergent propagation algorithms via oriented trees
 In UAI. 2007
"... 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 ..."
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Cited by 18 (3 self)
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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 TreeReweighted (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
Simultaneous Gate Sizing and Placement
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2000
"... In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased delay model to capture the timing constraints in the circuit. To reduce the problem size and improve the solution convergence, we iteratively identify and op ..."
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Cited by 13 (3 self)
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In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased 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 fanouts of the gates on the kmost critical paths; b) size down the immediate fanouts of the gates on the kmost critical paths; c) simultaneously reposition and resize the gates on the kmost 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
Genetic Algorithm in Search and Optimization: The Technique and Applications
 Proc. of Int. Workshop on Soft Computing and Intelligent Systems
, 1997
"... 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 ..."
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Cited by 6 (0 self)
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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 operatorsreproduction, 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 ...
A Unifying Investigation of InteriorPoint Methods for Convex Programming
 FACULTY OF MATHEMATICS AND INFORMATICS, TU DELFT, NL2628 BL
, 1992
"... In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorp ..."
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Cited by 5 (4 self)
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In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorpoint methods for these programs can thus be reduced to the analysis of interiorpoint methods with selfconcordant barrier functions.
M.Pedram “Gate sizing with controlled Displacement
 in Proceedings of international symposium on physical design
"... Abstract In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased delay model to capture the timing constraints in the circuit. To reduce the problem size and improve the solution convergence, we iteratively ident ..."
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Cited by 2 (1 self)
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Abstract In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased 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. All the operations are formulated and solved as mathematical programming problems 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
Artificial Immune System for Solving Generalized Geometric Problems: A Preliminary Results
"... Generalized geometric programming (GGP) is an optimization method in which the objective function and constraints are nonconvex functions. Thus, a GGP problem includes multiple local optima in its solution space. When using conventional nonlinear programming methods to solve a GGP problem, local opt ..."
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Cited by 1 (0 self)
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Generalized geometric programming (GGP) is an optimization method in which the objective function and constraints are nonconvex functions. Thus, a GGP problem includes multiple local optima in its solution space. When using conventional nonlinear programming methods to solve a GGP problem, local optimum may be found, or the procedure may be mathematically tedious. To find the global optimum of a GGP problem, a bioimmunebased approach is considered. This study presents an artificial immune system (AIS) including: an operator to control the number of antigenspecific antibodies based on an idiotypic network hypothesis; an editing operator of receptor with a Cauchy distributed random number, and a bone marrow operator used to generate diverse antibodies. The AIS method was tested with a set of published GGP problems, and their solutions were compared with the known global GGP solutions. The testing results show that the proposed approach potentially converges to the global solutions.