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15
TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 35 (8 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
A Globally Convergent PrimalDual InteriorPoint Filter Method for Nonlinear Programming
, 2002
"... In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the p ..."
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Cited by 33 (4 self)
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In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the perturbed firstorder necessary conditions into a normal and a tangential step, whose sizes are controlled by a trustregion type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to firstorder critical points is proved for the new primaldual interiorpoint filter algorithm.
Supervised detection of regulatory motifs in DNA sequences
 STATISTICAL APPLICATIONS IN GENETICS AND MOLECULAR BIOLOGY
, 2003
"... Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs motif sampler) model binding sites as ..."
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Cited by 6 (1 self)
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Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs motif sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from structural characteristics of proteinDNA interactions. We extend the simple multinomial mixture model to a constrained multinomial mixture model by incorporating constraints on the information content profiles or on specific parameters of the motif PWMs. The parameters of this extended model are estimated by maximum likelihood using a nonlinear constraint optimization method. Likelihoodbased crossvalidation is used to select model parameters such as motif width and constraint type. The performance of COMODE is compared with existing motif detection methods on simulated data that incorporate real motif examples from Saccharomyces cerevisiae. The proposed method is especially effective when the motif of interest appears as a weak signal in the data. Some of the transcription factor binding data of Lee et al. (2002) were also analyzed using COMODE and biologically verified sites were identified.
On the Convergence of a Trust Region SQP Algorithm for Nonlinearly Constrained Optimization Problems
, 1995
"... In (Boggs, Tolle and Kearsley 1994b) the authors introduced an effective algorithm for general large scale nonlinear programming problems. In this paper we describe the theoretical foundation for this method. The algorithm is based on a trust region, sequential quadratic programming (SQP) technique ..."
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Cited by 2 (2 self)
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In (Boggs, Tolle and Kearsley 1994b) the authors introduced an effective algorithm for general large scale nonlinear programming problems. In this paper we describe the theoretical foundation for this method. The algorithm is based on a trust region, sequential quadratic programming (SQP) technique and uses a special auxiliary function, called a merit function or linesearch function, for assessing the steps that are generated. A global convergence theorem for a basic version of the algorithm is stated and its proof is outlined.
Linear Processing and Sum Throughput in the Multiuser MIMO Downlink Adam J. Tenenbaum
, 811
"... We consider linear precoding and decoding in the downlink of a multiuser multipleinput, multipleoutput (MIMO) system, wherein each user may receive more than one data stream. We propose several mean squared error (MSE) based criteria for joint transmitreceive optimization and establish a series of ..."
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Cited by 2 (0 self)
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We consider linear precoding and decoding in the downlink of a multiuser multipleinput, multipleoutput (MIMO) system, wherein each user may receive more than one data stream. We propose several mean squared error (MSE) based criteria for joint transmitreceive optimization and establish a series of relationships linking these criteria to the signaltointerferenceplusnoise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. In particular, we show that achieving the maximum sum throughput is equivalent to minimizing the product of MSE matrix determinants (PDetMSE). Since the PDetMSE minimization problem does not admit a computationally efficient solution, a simplified scalar version of the problem is considered that minimizes the product of mean squared errors (PMSE). An iterative algorithm is proposed to solve the PMSE problem, and is shown to provide nearoptimal performance with greatly reduced computational complexity. Our simulations compare the achievable sum rates under linear precoding strategies to the sum capacity for the broadcast channel. I.
Sum Rate Maximization using Linear Precoding and Decoding in the Multiuser MIMO Downlink
, 801
"... Abstract—We propose an algorithm to maximize the instantaneous sum data rate transmitted by a base station in the downlink of a multiuser multipleinput, multipleoutput system. The transmitter and the receivers may each be equipped with multiple antennas and each user may receive more than one data ..."
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Cited by 1 (0 self)
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Abstract—We propose an algorithm to maximize the instantaneous sum data rate transmitted by a base station in the downlink of a multiuser multipleinput, multipleoutput system. The transmitter and the receivers may each be equipped with multiple antennas and each user may receive more than one data stream. We show that maximizing the sum rate is closely linked to minimizing the product of mean squared errors (PMSE). The algorithm employs an uplink/downlink duality to iteratively design transmitreceive linear precoders, decoders, and power allocations that minimize the PMSE for all data streams under a sum power constraint. Numerical simulations illustrate the effectiveness of the algorithm and support the use of the PMSE criterion in maximizing the overall instantaneous data rate. I.
SIMULATIONBASED OPTIMIZATION STRATEGY FOR LIQUID FUELED MULTISTAGE SPACE LAUNCH VEHICLE
"... The optimal design of launch vehicles based on liquid rocket engines is critically dependent on ascent trajectories and thrust throttling. Recently many authors have incorporated trajectory optimization at conceptual design level but still have not gauged the potential of using thrust throttling at ..."
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The optimal design of launch vehicles based on liquid rocket engines is critically dependent on ascent trajectories and thrust throttling. Recently many authors have incorporated trajectory optimization at conceptual design level but still have not gauged the potential of using thrust throttling at conceptual design phase. In this study we propose not only the trajectory optimization but also the thrust throttling at the conceptual design phase. This newly formulation problem is solved through hybrid optimization algorithm using Genetic Algorithm as global optimizer and Sequential Quadratic Programming as local optimizer starting from the solution given by Genetic Algorithm. The objective is to find minimum gross launch weight (GLW), optimal trajectory and thrust throttling profile for liquid fueled space launch vehicle (SLV). The improvement in system design using thrust throttling is studied in detail. 1.
Infinitedimensional Optimization and Optimal Design
, 2003
"... Formulation In the most general form, we can write an optimization problem in a topological space endowed with some topology and J : R is the objective functional. By extending the objective functional to U via J(u) := we can rewrite this problem as . ..."
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Formulation In the most general form, we can write an optimization problem in a topological space endowed with some topology and J : R is the objective functional. By extending the objective functional to U via J(u) := we can rewrite this problem as .