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sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure
 In Recent advances in LMI methods for control
, 1995
"... . A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet pr ..."
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Cited by 46 (19 self)
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. A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet problems). These problems often have matrix structure, i.e., some of the optimization variables are matrices. This matrix structure has two important practical ramifications: first, it makes the job of translating the problem into a standard SDP or maxdet format tedious, and, second, it opens the possibility of exploiting the structure to speed up the computation. In this paper we describe the design and implementation of sdpsol, a parser/solver for SDPs and maxdet problems. sdpsol allows problems with matrix structure to be described in a simple, natural, and convenient way. Although the current implementation of sdpsol does not exploit matrix structure in the solution algorithm, the languag...
Antenna Array Pattern Synthesis via Convex Optimization
, 1997
"... 'We show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems, which can be (numerically) solved with great efficiency by recently developed interiorpoint methods. The synthesis problems involve arrays with arbitrary geometry and element direct ..."
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Cited by 37 (8 self)
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'We show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems, which can be (numerically) solved with great efficiency by recently developed interiorpoint methods. The synthesis problems involve arrays with arbitrary geometry and element directivity, constraints on far and nearfield patterns over narrow or broad frequency bandwidth, and some important robustness constraints. We show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays.
Optimal Wire and Transistor Sizing for Circuits with NonTree Topology
 in Proc. Int. Conf. on Computer Aided Design
, 1997
"... Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree ..."
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Cited by 28 (11 self)
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Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to highperformance deep submicron design including, for example, circuits with loops of resistors, e.g., clock distribution meshes, and circuits with coupling capacitors, e.g., buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently developed efficient interi...
Optimizing dominant time constant in RC circuits
, 1996
"... We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interestin ..."
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Cited by 16 (8 self)
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We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interesting design problems as convex optimization problems, specifically, semidefinite programs (SDPs). For example, assuming that the conductances and capacitances are affine functions of the design parameters (which is a common model in transistor or interconnect wire sizing), one can minimize the power consumption or the area subject to an upper bound on the dominant time constant, or compute the optimal tradeoff surface between power, dominant time constant, and area. We will also note that, to a certain extent, convex optimization can be used to design the topology of the interconnect wires. This approach has two advantages over methods based on Elmore delay optimization. First, it handles a far wider class of circuits, e.g., those with nongrounded capacitors. Second, it always results in convex optimization problems for which very efficient interiorpoint methods have recently been developed. We illustrate the method, and extensions, with several examples involving optimal wire and transistor sizing.
FIR Filter Design via Semidefinite Programming and Spectral Factorization
, 1996
"... We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint metho ..."
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Cited by 15 (6 self)
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We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint methods. Using this LMI formulation, we can cast several interesting filter design problems as convex or quasiconvex optimization problems, e.g., minimizing the length of the FIR filter and computing the Chebychev approximation of a desired power spectrum or a desired frequency response magnitude on a logarithmic scale.
PAR Reduction in Multicarrier Transmission Systems
 ANSI Document, T1E1.4 Technical Subcommittee
, 1998
"... This contribution, which is based on [1], proposes a new family of methods to reduce Peak to Average power Ratio (PAR) in Discrete MultiTone (DMT) and Orthogonal Frequency Division Multiplexing (OFDM) systems. This new family of algorithms can be applied with different levels of complexity and perfo ..."
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Cited by 13 (5 self)
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This contribution, which is based on [1], proposes a new family of methods to reduce Peak to Average power Ratio (PAR) in Discrete MultiTone (DMT) and Orthogonal Frequency Division Multiplexing (OFDM) systems. This new family of algorithms can be applied with different levels of complexity and performance depending on our application constraints. Using the low complexity algorithms in our family, we can achieve 3dB of PAR reduction with 2N multiply /adds per DMT symbol and a data rate loss of less than :2%, or achieve 4dB of PAR reduction with 6N multiply/adds per symbol and a data rate loss of less than 1%. At higher complexity, 6 \Gamma 10dB of PAR reduction can be achieved for NlogN complexity per symbol. Tellado, J. and Cioffi, J.M.PAR Reduction: 2 1 Introduction The high peaktoaverage ratio of 15 dB in the Issue 1 and Issue 2 T1.413 ADSL standard DMT transmission technology has led to significant contributions on a variety of creative methods to reduce PAR [2, 3, 4, 5, 6, ...
Efficient Solution of Linear Matrix Inequalities for Integral Quadratic Constraints
 In Proc. IEEE Conf. on Decision and Control
, 2000
"... In this article is discussed how to implement an efficient interiorpoint algorithm for the semidefinite programs that result from integral quadratic constraints. The algorithm is a primaldual potential reduction method, and the computational effort is dominated by a leastsquares system that has ..."
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Cited by 9 (0 self)
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In this article is discussed how to implement an efficient interiorpoint algorithm for the semidefinite programs that result from integral quadratic constraints. The algorithm is a primaldual potential reduction method, and the computational effort is dominated by a leastsquares system that has to be solved in each iteration. The key to an efficient implementation is to utilize iterative methods and the specific structure of integral quadratic constraints. The algorithm has been implemented in Matlab. To give a rough idea of the efficiencies obtained, it is possible to solve problems resulting in a linear matrix inequality of dimension 130 #130 with approximately 5000 variables in about 10 minutes on a laptop. Problems with approximately 20000 variable and a linear matrix inequality of dimension 230 # 230 are solved in a few hours. It is not assumed that the system matrix has no eigenvalues on the imaginary axis, nor is it assumed that it is Hurwitz. Key Words: Linear Matrix Ineq...
Control applications of nonlinear convex programming
 the 1997 IFAC Conference on Advanced Process Control
, 1998
"... Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonline ..."
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Cited by 6 (3 self)
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Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interiorpoint algorithms for problem classes such as semide nite programming (SDP) or secondorder cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust openloop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the setpoint and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at