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BIOMETRIKA 2020年第1期107卷 191-204页

作者： Duan, Leo L. Young, Alexander L. Nishimura, Akihiko Dunson, David B. Univ Florida Dept Stat 101C Griffin Floyd HallPOB 118545 Gainesville FL 32611 USA Duke Univ Dept Stat Sci Box 90251 Durham NC 27708 USA Univ Calif Los Angeles Dept Stat 8125 Math Sci Bldg Los Angeles CA 90095 USA

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.

关键词： Constrained Bayes constraint function Factor model Manifold constraint Ordered simplex Orthonormality Parameter restriction Shrinkage

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SUPER-LINEARLY CONVERGENT QUASI-NEWTON ALGORITHMS FOR NONLINEARLY CONSTRAINED OPTIMIZATION PROBLEMS

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MATHEMATICAL PROGRAMMING 1976年第1期11卷 1-13页

作者： PALOMARES, UMG MANGASARIAN, OL UNIV WISCONSIN MADISON WI 53706 USA

A class of algorithms for nonlinearly constrained optimization problems is proposed. The subproblems of the algorithms are linearly constrained quadratic minimization problems which contain an updated estimate of the Hessian of the Lagrangian. Under suitable conditions and updating schemes local convergence and a superlinear rate of convergence are established. The convergence proofs require among other things twice differentiable objective and constraint functions, while the calculations use only first derivative data. Rapid convergence has been obtained in a number of test problems by using a program based on the algorithms proposed here.

关键词： Mathematical Method Test Problem Minimization Problem Suitable Condition constraint function

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NECESSARY AND SUFFICIENT CONDITIONS FOR A PENALTY METHOD TO BE EXACT

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MATHEMATICAL PROGRAMMING 1975年第1期9卷 87-99页

作者： BERTSEKAS, DP UNIV ILLINOIS URBANAIL 61801

This paper identifies necessary and sufficient conditions for a penalty method to yield an optimal solution or a Lagrange multiplier of a convex programming problem by means of a single unconstrained minimization. The conditions are given in terms of properties of the objective and constraint functions of the problem as well as the penalty function adopted. It is shown among other things that all linear programs with finite optimal value satisfy such conditions when the penalty function is quadratic.

关键词： Mathematical Method Lagrange Multiplier Programming Problem Penalty function constraint function

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Intravoxel Incoherent Motion Diffusion-Weighted MRI of the Abdomen: The Effect of Fitting Algorithms on the Accuracy and Reliability of the Parameters

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JOURNAL OF MAGNETIC RESONANCE IMAGING 2017年第6期45卷 1637-1647页

作者： Park, Hyo Jung Sung, Yu Sub Lee, Seung Soo Lee, Yedaun Cheong, Hyunhee Kim, Yeong Jae Lee, Moon-gyu Univ Ulsan Dept Radiol Coll Med Asan Med Ctr 88 Olympic Ro 43 Gil Seoul 138736 South Korea Univ Ulsan Res Inst Radiol Coll Med Asan Med Ctr 88 Olymp Ro 43 Gil Seoul 138736 South Korea Inje Univ Coll Med Haeundae Paik Hosp Dept Radiol Busan South Korea

Purpose To evaluate the influence of fitting methods on the accuracy and reliability of intravoxel incoherent motion (IVIM) parameters, with a particular emphasis on the constraint function. Materials and Methods Diffusion-weighted (DW) imaging data were analyzed using IVIM-based full-fitting (simultaneous fit of all parameters) and segmented-fitting (step-by-step fit of each parameter), each with and without the constraint function, to estimate the molecular diffusion coefficient (D-slow), perfusion fraction (f), and flow-related diffusion coefficient (D-fast). Computational simulations were performed at variable signal-to-noise ratios to evaluate the relative error (RE) and coefficient of variation (CV) of the estimated IVIM parameters. DW imaging of the abdomen was performed twice at 1.5 Tesla using nine b-values (0-900 s/mm(2)) in 12 health volunteers (6 men and 6 women;mean age: 30 years). The measurement repeatability of IVIM parameters in the liver and the pancreas was evaluated using the within-subject coefficient of variation (wCV). ResultsIn simulations, full-fitting without the constraint function yielded the largest RE (P<0.001 for D-slow and f;P < 0.044 for D-fast) and CV (P < 0.033 for D-slow and f;P < 0.473 for D-fast) for IVIM parameters among all four algorithms. In volunteer imaging, full-fitting without the constraint function also resulted in the poorest repeatability for D-slow (wCV, 17.12%-65.45%) and f (wCV, 19.35%-42.84%) in the liver and pancreas, while the other algorithms had similar repeatability values (wCV, 4.05%-11.99% for D-slow and 9.65%-18.66% for f). Measurement repeatability of D-fast (wCV, 29.52%-85.01%) was the poorest among the IVIM parameters. Conclusion For accurate and reliable measurement of IVIM parameters, segmented fitting or full-fitting with the constraint function should be used for IVIM-based analysis of DW imaging.

关键词： constraint function diffusion-weighted imaging intra-voxel incoherent motion in vivo magnetic resonance imaging Monte Carlo simulation

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A Lagrangian Property for Homogeneous Programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1973年第1期12卷 99-102页

作者： Greenberg, H. J. So Methodist Univ Inst Technol Comp Sci Operat Res Ctr Dallas TX 75275 USA

Euler's equation is applied to the response function of a mathematical program whose maximand and constraint functions are positively homogeneous over the policy cone. An algorithmic advantage (sing GLM) is cited,... 详细信息

关键词： constraint function Geometric Program Single constraint Policy Cone Lagrangian Property

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Differentiability of the constraint functions in Probabilistic Constrained Programs

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Optimization 1989年第4期20卷 509-515页

作者： Wang, J. Nanjing University Dept. of Mathematics China

This paper is devoted to study of differentiability of the constraint functions in probabilistic constrained programs. Explicit formulae for the gradient or the directional derivatives are given. © 1989, Taylor &... 详细信息

关键词： constraint function Differentiability Probabilistic constrained program

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Approximation methods for optimal network coding in a multi-hop control network with packet losses

Approximation methods for optimal network coding in a multi-...

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European Control Conference (ECC)

作者： Smarra, F. D'Innocenzo, A. Di Benedetto, M. D. Univ Aquila Dept Informat Engn Comp Sci & Math Ctr Excellence DEWS Nucleo Ind Pile Via G Gronchi 18 I-67100 Laquila Italy

ISBN: (纸本)9783952426937

A Multi-hop Control Network consists of a plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. With the aim of rendering the system robust with respect to packet losses, we exploit network coding and redundancy in data communication (i.e. sending multiple copies of sensing and actuation data via multiple routing paths associated to possibly different delays) and assume that such data is re-combined as a weighed linear combination. The main contribution of this paper is to provide efficient computational methods to find the optimal choice of such weights either to maximize or to constrain a robustness metric based on the notion of Asymptotic Mean Square Stability. Since we observe that such metric induces an objective or constraint function that is highly non-linear, we propose an approximation that takes into account both the network parameters and the system dynamics: it is based on the assumption that packet loss probabilities are much smaller than correct transmission probabilities and leverages the well known Gerschgorin disks. We then compare our approximation with the optimal choice from the communication designer point of view, which neglects the system dynamics and is based on the idea of minimizing the quadratic error induced by the network on the actuation signal. The comparison of the above approximations quantitatively shows that the optimal choices from the points of view of control and communication theory are often at odds.

关键词： approximation theory asymptotic stability control system synthesis mean square error methods network coding networked control systems optimal control radio networks redundancy robust control telecommunication network routing Gerschgorin disks actuation data actuation signal actuators approximation method asymptotic mean square stability computational methods computational units constraint function data communication data flow multihop control network multiple routing paths network parameters nonlinear parameters objective function optimal choice optimal network coding packet loss probabilities quadratic error minimization quantitative analysis robustness metric scheduling sensing data sensors system dynamics wireless multihop communication network Actuators Delays Markov processes Packet loss Spread spectrum communication Wireless sensor networks

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Compressive Sampling and Reconstruction of ECG Signal for Manned Spaceflight Applications 4

Compressive Sampling and Reconstruction of ECG Signal for Ma...

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4th IEEE International Conference on Recent Trends on Electronics, Information, Communication and Technology (RTEICT)

作者： Anand, P. M. Thiruppathirajan, S. Shajahan, E. S. Sreekumar, S. Vinod, P. Narayana, Namboodiripad M. Indian Space Res Org Baseband Syst Elect Div Vikram Sarabhai Space Ctr Trivandrum Kerala India Coll Engn Dept Elect Trivandrum Kerala India Indian Space Res Org Vikram Sarabhai Space Ctr Digital Syst Grp Trivandrum Kerala India Indian Space Res Org Vikram Sarabhai Space Ctr Avion Entity Trivandrum Kerala India

ISBN: (纸本)9781728106304;9781728106311

Electrocardiogram (ECG) is a vital signal which represents the state of health of astronauts in a manned spaceflight mission and hence must be continuously acquired and transmitted throughout the mission. Telemetry bandwidth is a premium resource in such applications. Traditional method of sampling at Nyquist rate is highly bandwidth inefficient. Hence it is advantageous to use Compressive sensing (CS) technique to optimize data at measurement point itself. Conventional CS techniques employ computationally intensive measurement matrices which are not hardware efficient for both acquisition as well as recovery. In this work, a hardware efficient scheme with use of a sparse binary measurement matrix is proposed. The signal is recovered from the compressive measurement using a constraint function based on inverted Laplace distribution function. Gradient decent method is used to recursively recover the original ECG signal from the compressive measurements in an efficient manner. Apart from this, a projection scheme is also proposed to minimize the recovery error. The proposed scheme was extensively evaluated with different ECG samples with different compression ratios. Finally, the proposed scheme was benchmarked with Approximated L0 norm based method and it is found to perform more efficiently in compressively sensing and recovery of ECG signals.

关键词： Electrocardiogram (ECG) compressed sensing (CS) discrete cosine transform (DCT) constraint function

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Optimizing PID Controller Tuning for Greenhouse Lighting Control System by Varying Number of Objectives

Optimizing PID Controller Tuning for Greenhouse Lighting Con...

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11th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology

作者： Mahdavian, Mehdi Wattanapongsakorn, Naruemon King Mongkuts Univ Technol Thonburi Dept Comp Engn Bangkok 10140 Thailand

ISBN: (纸本)9781479929931

Nowadays, usage of optimization methods and techniques in various applications is the key factor of increasing the systems efficiency and performance. In this paper, Proportional-Integral-Derivative (PID) controller optimization in greenhouse lighting control system is studied by tuning PID controller coefficients. The advantages and disadvantages of employing multi-objective optimization methods have been discussed in many cases by researchers and engineers. In this regard, we consider the optimizing problem with varying number of objectives which are 1, 2 and 3 objectives. The simulation results verify that the improvement of the system output responses would be achieved by increasing the number of separated and independent objective functions.

关键词： greenhouse lighting control system proportional-integral-derivative (PID) controller objective function constraint function single-objective optimization multi-objective optimization

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A Kind of Optimization model on turning process Based on productivity and cost

A Kind of Optimization model on turning process Based on pro...

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3rd International Conference on Advances in Materials Manufacturing (ICAMMP 2012)

作者： Yan, Wei Fan, Jun Guo, Xufeng Sichuan Vocat & Tech Coll Commun Chengdu Peoples R China

ISBN: (纸本)9783037856208

The machine processing optimization model is one kind of typical restraint optimization model. This paper takes the lathe work as an example to study the construction way of optimization model construction under a series of constraint environments, and its goal is pursues the highest productivity and the lowest cost. The purpose of machine optimal-adaptive control system is to pursue the highest efficiency and lowest processing cost under existing manufacture background that is seeking for the greatest economic efficiency. So that, the goal of optimization model constructing usually is the highest productivity, the lowest cost or the maximum profit. But in actual machining procedure, because of restrain of processing equipment, the working condition as well as the work piece material, its optimal process will have be restrained by a series of environment condition, therefore, resulting in that machine processing optimization model is one kind of typical restraint optimization model. This paper studies the optimization model construction for lathe machining under a series of constraint environments condition, and its goal is pursues the highest productivity and the lowest cost.

关键词： optimized model objective function constraint function turning process

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