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12
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
Semidefinite Programming and Integer Programming
"... We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems. ..."
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Cited by 48 (7 self)
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We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems.
On The PrimalDual Geometry Of Level Sets in Linear and Conic Optimization
, 2001
"... For a conic optimization problem P: minimize x c ..."
FenchelLagrange versus Geometric Duality in Convex Optimization
"... We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve st ..."
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Cited by 5 (4 self)
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We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve strong duality are considered and optimality conditions are derived. Next we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions in order to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach we present.
Proving Strong Duality for Geometric Optimization Using a Conic Formulation
, 1999
"... Geometric optimization is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the wellknown associated duality theory, using conic optimization. After introducing suitable convex cones and studying their ..."
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Cited by 5 (1 self)
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Geometric optimization is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the wellknown associated duality theory, using conic optimization. After introducing suitable convex cones and studying their properties, we model geometric optimization problems with a conic formulation, which allows us to apply the powerful duality theory of conic optimization and derive the duality results valid for geometric optimization.
Improving Complexity of Structured Convex Optimization Problems Using SelfConcordant Barriers
, 2001
"... The purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using to the theory of selfconcordant functions developed in [11]. We describe the classical shortstep interiorpoint method and optimize its parameters in order to pr ..."
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Cited by 2 (0 self)
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The purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using to the theory of selfconcordant functions developed in [11]. We describe the classical shortstep interiorpoint method and optimize its parameters in order to provide the best possible iteration bound. We also discuss the necessity of introducing two parameters in the definition of selfconcordancy and which one is the best to fix. A lemma from [3] is improved, which allows us to review several classes of structured convex optimization problems and improve the corresponding complexity results.
Geometric dual formulation for firstderivativebased univariate cubic L1 splines
 J. Global Optim
"... With the objective of generating “shapepreserving ” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of firstderivativebased C 1smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between t ..."
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Cited by 1 (1 self)
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With the objective of generating “shapepreserving ” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of firstderivativebased C 1smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between the firstorder derivative of the spline and the local divided difference of the data. Calculating the coefficients of an L1 spline is a nonsmooth nonlinear convex program. Via Fenchel’s conjugate transformation, the geometric dual program is a smooth convex program with a linear objective function and convex cubic constraints. The dualtoprimal transformation is accomplished by solving a linear program. Key words. Conjugate function, convex program, cubic L1 spline, shapepreserving interpolation, piecewise polynomial.
An Extended Conic Formulation for Geometric Optimization
, 2000
"... The author has recently proposed a new way of formulating two classical classes of structured convex problems, geometric and l p norm optimization, using dedicated convex cones [Gli99, GT00]. This approach has some advantages over the traditional formulation: it simplifies the proofs of the wellkn ..."
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The author has recently proposed a new way of formulating two classical classes of structured convex problems, geometric and l p norm optimization, using dedicated convex cones [Gli99, GT00]. This approach has some advantages over the traditional formulation: it simplifies the proofs of the wellknown associated duality properties (i.e. weak and strong duality) and the design of a polynomial algorithm becomes straightforward. These new proofs rely on the general duality theory valid for convex problems expressed in conic form [SW70, Stu00] and the work on polynomial interiorpoint methods by Nesterov and Nemirovsky [NN94]. In this paper, we make a step towards the description of a common framework that would include these two classes of problems. Indeed, we introduce an extended variant of the cone for geometric optimization used in [Gli99] and show it is equally suitable to formulate this class of problems. This new cone has the additional advantage of being very similar to the ...
Approximating Geometric Optimization with l_pNorm Optimization
, 2000
"... In this article, we demonstrate how to approximate geometric optimization with l p  norm optimization. These two categories of problems are well known in structured convex optimization. We describe a family of l p norm optimization problems that can be made arbitrarily close to a geometric optimiz ..."
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In this article, we demonstrate how to approximate geometric optimization with l p  norm optimization. These two categories of problems are well known in structured convex optimization. We describe a family of l p norm optimization problems that can be made arbitrarily close to a geometric optimization problem, and show that the dual problems for these approximations are also approximating the dual geometric optimization problem. Finally, we use these approximations and the duality theory for l p norm optimization to derive simple proofs of the weak and strong duality theorems for geometric optimization.