Results 1  10
of
17
Basis Pursuit
, 1994
"... The TimeFrequency and TimeScale communities have recently developed an enormous number of overcomplete signal dictionaries  wavelets, wavelet packets, cosine packets, wilson bases, chirplets, warped bases, and hyperbolic cross bases being a few examples. Basis Pursuit is a technique for decompos ..."
Abstract

Cited by 119 (15 self)
 Add to MetaCart
The TimeFrequency and TimeScale communities have recently developed an enormous number of overcomplete signal dictionaries  wavelets, wavelet packets, cosine packets, wilson bases, chirplets, warped bases, and hyperbolic cross bases being a few examples. Basis Pursuit is a technique for decomposing a signal into an "optimal" superposition of dictionary elements. The optimization criterion is the l 1 norm of coefficients. The method has several advantages over Matching Pursuit and Best Ortho Basis, including superresolution and stability. 1 Introduction Over the last five years or so, there has been an explosion of awareness of alternatives to traditional signal representations. Instead of just representing objects as superpositions of sinusoids (the traditional Fourier representation) we now have available alternate dictionaries  signal representation schemes  of which the Wavelets dictionary is only the most wellknown. Wavelet dictionaries, Gabor dictionaries, Multiscale...
Efficient Convex Optimization For Engineering Design
, 1994
"... . Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a highlevel description of recently developed interiorpoint methods for convex optimization, explain how problem structure can be exploited in these algori ..."
Abstract

Cited by 21 (13 self)
 Add to MetaCart
. Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a highlevel description of recently developed interiorpoint methods for convex optimization, explain how problem structure can be exploited in these algorithms, and illustrate the general scheme with numerical experiments. To give a rough idea of the efficiencies obtained, we are able to solve convex optimization problems with over 1000 variables and 10000 constraints in around 10 minutes on a workstation. Keywords. Optimization, numerical methods, linear programming, optimal control, robust control, convex programming, interiorpoint methods, FIR filter design, conjugate gradients 1. INTRODUCTION Many problems in engineering analysis and design can be cast as convex optimization problems, i.e., min f 0 (x) s.t. f i (x) 0; i = 1; : : : ; L; where the functions f i are convex. It is widely known that such problems have desirable properties,...
Primaldual projected gradient algorithms for extended linearquadratic programming
 SIAM J. Optimization
"... Abstract. Many largescale problems in dynamic and stochastic optimization can be modeled with extended linearquadratic programming, which admits penalty terms and treats them through duality. In general the objective functions in such problems are only piecewise smooth and must be minimized or max ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
Abstract. Many largescale problems in dynamic and stochastic optimization can be modeled with extended linearquadratic programming, which admits penalty terms and treats them through duality. In general the objective functions in such problems are only piecewise smooth and must be minimized or maximized relative to polyhedral sets of high dimensionality. This paper proposes a new class of numerical methods for “fully quadratic ” problems within this framework, which exhibit secondorder nonsmoothness. These methods, combining the idea of finiteenvelope representation with that of modified gradient projection, work with local structure in the primal and dual problems simultaneously, feeding information back and forth to trigger advantageous restarts. Versions resembling steepest descent methods and conjugate gradient methods are presented. When a positive threshold of εoptimality is specified, both methods converge in a finite number of iterations. With threshold 0, it is shown under mild assumptions that the steepest descent version converges linearly, while the conjugate gradient version still has a finite termination property. The algorithms are designed to exploit features of primal and dual decomposability of the Lagrangian, which are typically available in a largescale setting, and they are open to considerable parallelization. Key words. Extended linearquadratic programming, largescale numerical optimization, finiteenvelope representation, gradient projection, primaldual methods, steepest descent methods, conjugate gradient methods. AMS(MOS) subject classifications. 65K05, 65K10, 90C20 1. Introduction. A
User’s Guide For QPOPT 1.0: A Fortran Package For Quadratic Programming
, 1995
"... QPOPT is a set of Fortran subroutines for minimizing a general quadratic function subject to linear constraints and simple upper and lower bounds. QPOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. If the quadratic function ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
QPOPT is a set of Fortran subroutines for minimizing a general quadratic function subject to linear constraints and simple upper and lower bounds. QPOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. If the quadratic function is convex (i.e., the Hessian is positive definite or positive semidefinite), the solution obtained will be a global minimizer. If the quadratic is nonconvex (i.e., the Hessian is indefinite), the solution obtained will be a local minimizer or a deadpoint. A twophase activeset method is used. The first phase minimizes the sum of infeasibilities. The second phase minimizes the quadratic function within the feasible region, using a reduced Hessian to obtain search directions. The method is most efficient when many constraints or bounds are active at the solution. QPOPT is not intended for large sparse problems, but there is no fixed limit on problem size. The source code is suitable for all scientific machines with a Fortran 77
A Variant of the TopkisVeinott Method for Solving Inequality Constrained Optimization Problems
 J. Appl. Math. Optim
, 1997
"... . In this paper, we give a variant of the TopkisVeinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
. In this paper, we give a variant of the TopkisVeinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a FritzJohn point of the problem. We introduce a FritzJohn (FJ) function, an FJ1 strong secondorder sufficiency condition (FJ1SSOSC) and an FJ2 strong secondorder sufficiency condition (FJ2SSOSC), and then show, without any constraint qualification (CQ), that (i) if an FJ point z satisfies the FJ1SSOSC, then there exists a neighborhood N(z) of z such that for any FJ point y 2 N(z) n fzg, f 0 (y) 6= f 0 (z), where f 0 is the objective function of the problem; (ii) if an FJ point z satisfies the FJ2SSOSC, then z is a strict local minimum of the problem. The resu...
MinimumTime Control Characteristics of Flexible Structures
 J. Guid., Ctrl
, 1996
"... The timeoptimal control of flexible structures is considered. We formulate the general timeoptimal control problem for singleaxis flexible structures, and analytical results are given for the number of control switches for the onebendingmode case, with and without damping. When there is no damp ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
The timeoptimal control of flexible structures is considered. We formulate the general timeoptimal control problem for singleaxis flexible structures, and analytical results are given for the number of control switches for the onebendingmode case, with and without damping. When there is no damping, it is shown that the time optimal control generally has 3 switches and is an odd function of time about the second switch except in certain isolated cases where there is only 1 switch. With damping, it is shown that there is always more than 1 switch. A numerical method is presented for solving the timeoptimal control for general linear systems, and solutions are presented for flexible structures with several flexible modes, revealing interesting trends of the timeoptimal control switch times as the maneuver sizes and the frequencies and damping ratios of the flexible modes are varied. 1 Introduction In many applications, such as manipulators, diskdrive heads, or pointing systems, s...
Optimization of Wafer Temperature Uniformity in Rapid Thermal Processing Systems
 SUBMITTED TO IEEE TRANSACTIONS ON ELECTRON DEVICES
, 1991
"... During rapid thermal processing (RTP) of semiconductor wafers it is essential that the wafer temperature closely tracks a prespecified temperature trajectory and that the temperature profile across the wafer is nearly uniform whenever the wafer is at high temperatures. This paper considers axisymm ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
During rapid thermal processing (RTP) of semiconductor wafers it is essential that the wafer temperature closely tracks a prespecified temperature trajectory and that the temperature profile across the wafer is nearly uniform whenever the wafer is at high temperatures. This paper considers axisymmetric RTP systems with multiple independentlycontrollable lamps. In such systems the relative lamp power settings can be adjusted so that the lamps provide a range of distributions of power over the wafer; this is useful because the ideal distribution of incident energy varies according to processing conditions and changes substantially during a single process cycle. In this paper numerical techniques are given for finding lamp power settings to minimize temperature error across the wafer both during steadystate hold and during transients; these numerical techniques involve the formulation of the minimum temperature error problem as a linear programming problem. A heuristic scheme for nearoptimal trajectory following is presented. Openloopplusfeedback control is proposed for RTP temperature control  openloop control allows precise trajectory planning and feedback prevents drift due to disturbances and modeling errors. All of the above ideas are demonstrated in simulation on a fictional system qualitatively similar in its behavior to some real RTP systems.
Exponential Families
, 1990
"... General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood es ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood estimation. The first, the "phase I " algorithm determines the support of the MLE in the closure of the exponential family (a distribution in the family conditioned on a face of the convex support of the natural statistic) when the MLE does not exist in the traditional sense (a point in the natural parameter space). The second, the maximum Monte Carlo likelihood algorithm uses the Metropolis algorithm or the Gibbs sampler to obtain estimates when exact calculation of the likelihood is not possible. Separate papers on each algorithm accompany
Variable Fusion: A New Adaptive Signal Regression Method
, 1997
"... Signal and image processing are active areas of research in both statistics and engineering. Most of this research has emphasized the reconstruction of a "true" underlying pattern from one measured with noise. Our research has a different goal: recognition or prediction of an ancillary quantity y ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Signal and image processing are active areas of research in both statistics and engineering. Most of this research has emphasized the reconstruction of a "true" underlying pattern from one measured with noise. Our research has a different goal: recognition or prediction of an ancillary quantity y associated with each observed pattern x(t). We propose a nonlinear regularized regression technique, variable fusion. Variable fusion produces models of a simple parsimonious form, readily explained to the nonstatistician and possibly affording savings in data collection. In addition, variable fusion models perform well in terms of prediction. In this paper we assume that the quantity y is real and singlevalued and the pattern x(t) is a "signal", i.e., the space of index values t is onedimensional, although we describe the generalization of the method to a multidimensional index space. We use the patterns as the predictors of y. The patterns generally originate as analog signals an...
Optimization Framework for the Synthesis of Chemical Reactor Networks
, 1998
"... The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...