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Optimal design of acoustic metamaterial cloaks under uncertainty [article]

Peng Chen and Michael R. Haberman and Omar Ghattas
2020 arXiv   pre-print
To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random  ...  Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method's Hessian computation is viable for large,  ...  We next draw 10 random samples of the random variable ζ, and solve the scattering problem for each optimal design field.  ... 
arXiv:2007.13252v1 fatcat:o7rckgara5aupmb2kw2dj5lxbm

Solution of Stochastic Quadratic Programming with Imperfect Probability Distribution Using Nelder-Mead Simplex Method

Xinshun Ma, Xin Liu
2018 Journal of Applied Mathematics and Physics  
A direct optimizing algorithm based on Nelder-Mead simplex method is proposed for solving the problem. Finally, a numerical example is given to demonstrate the efficiency of the algorithm.  ...  Stochastic quadratic programming with recourse is one of the most important topics in the field of optimization.  ...  In recent years, with the introduction of new theories and methods for solving nonlinear equations, especially the infinite dimensional variational inequality theories and the application of smoothness  ... 
doi:10.4236/jamp.2018.65095 fatcat:p5suimiaijcibiot2digck2xbu

Model Predictive Control for Tracking of Underactuated Vessels Based on Recurrent Neural Networks

Zheng Yan, Jun Wang
2012 IEEE Journal of Oceanic Engineering  
In this paper, a model predictive control (MPC) scheme is presented for tracking of underactuated vessels with only two available controls: namely, surge force and yaw moment.  ...  When no external disturbance is explicitly considered, the proposed MPC approach iteratively solves a formulated quadratic programming (QP) problem using a single-layer recurrent neural network called  ...  In [32] , two neural networks with simple structures were applied for solving linear programming and QP problems for linear MPC.  ... 
doi:10.1109/joe.2012.2201797 fatcat:maoq3e3erbgstfy3o3qtdwna2u

Solving stochastic AC power flow via polynomial chaos expansion

Tillmann Muhlpfordt, Timm Faulwasser, Veit Hagenmeyer
2016 2016 IEEE Conference on Control Applications (CCA)  
For rectangular power flow, polynomial chaos expansion together with Galerkin projection yields a deterministic reformulation of the stochastic power flow problem that is solved numerically in a single  ...  it is computationally more efficient than Monte Carlo sampling.  ...  Monte Carlo methods require to solve the nominal problem for a large number of samples drawn from a set with a specified probability distribution, see [12] for a general introduction and [13] for results  ... 
doi:10.1109/cca.2016.7587824 dblp:conf/IEEEcca/MuhlpfordtFH16 fatcat:r52l6ijusbfrbmo7vror25z6gu

Combinatorial optimization of permutation-based quadratic assignment problem using optics inspired optimization

Soheila Badrloo, Ali Husseinzadeh Kashan
2019 Journal of Applied Research on Industrial Engineering  
The obtained results and its comparison with the solutions of the central library of Quadratic assignment problem (QAPLIB) show that the proposed algorithm can exactly solve small-sized problems with 100%  ...  Different exact methods are suggested to solve these problems, but because of the special structure of these problems, by increasing the size of the problem, finding an exact solution become more complicated  ...  [3] Integrated the Whale Algorithm with Tabu Search for solving quadratic assignment Problem.  ... 
doi:10.22105/jarie.2019.200177.1106 doaj:5c7a798e17a9401280ca8865b441e3e7 fatcat:ie6pnenbanew3eqrsa2hzltesm

Computing the Positive Stabilizing Solution to Algebraic Riccati Equations With an Indefinite Quadratic Term via a Recursive Method

Alexander Lanzon, Yantao Feng, Brian D. O. Anderson, Michael Rotkowitz
2008 IEEE Transactions on Automatic Control  
An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed.  ...  Index Terms-Algebraic Riccati equation (ARE), Riccati equations, indefinite quadratic term, iterative algorithms.  ...  Varga for providing insight into some of the motivational arguments presented in the introduction.  ... 
doi:10.1109/tac.2008.2006108 fatcat:mvt5xiuqs5cgfethqchg7h2wby

Bridging Parameter and Data Spaces for Fast Robust Estimation in Computer Vision

Alireza Bab-Hadiashar, Reza Hoseinnezhad
2008 2008 Digital Image Computing: Techniques and Applications  
method for its search.  ...  The proposed search involves replacing a p-tuple with another p-tuple in the data space, while moving towards the minimum point of the estimator's cost function in the parameter space.  ...  The seventies were an exciting time for resampling theories and the success of Efron's bootstrap technique [2] was perhaps an encouraging sign for the use of random sampling method for solving optimization  ... 
doi:10.1109/dicta.2008.10 dblp:conf/dicta/Bab-HadiasharH08 fatcat:zi4ye6gnpfhrpe4oyhu2koyovq

Contribution to Development of Reliability and Optimization Methods Applied to Mechanical Structures

Siham Ouhimmou, Abdelkhalak El Hami, Rachid Ellaia, Mohamed Tkiouat
2013 Applied Mathematics  
For this reason, we have combined the method SQP with the Multi start method.  ...  This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO).  ...  for global optimization can overcome some of the limitations of the local Solving method.  ... 
doi:10.4236/am.2013.41005 fatcat:qihsvvq6lzde3c5qvt4kazbpne

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Fani Boukouvala, Ruth Misener, Christodoulos A. Floudas
2016 European Journal of Operational Research  
Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems.  ...  This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO).  ...  An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions. Structural and Multidisciplinary Optimization 45 (1), 53-64.  ... 
doi:10.1016/j.ejor.2015.12.018 fatcat:jwe7b7ivrzhrjbttdl74eff2pe

Augmenting the bootstrap to analyze high dimensional genomic data

Svitlana Tyekucheva, Francesca Chiaromonte
2008 Test (Madrid)  
Svitlana Tyekucheva and Francesca Chiaromonte provide an attractive solution to the problem of the estimation of the inverse covariance matrix with high-dimensional data and small samples, which is an  ...  As pointed out in , PLS with a penalization term is equivalent to solving the normal equation with a preconditioning matrix that is defined as M = (I + P ) −1 , where P denotes a penalty matrix.  ...  In the same vein, Binder and Schumacher (2007) show that complexity selection in bootstrap samples drawn with replacement is biased towards more complex models in many settings.  ... 
doi:10.1007/s11749-008-0098-6 fatcat:yuq2vu5dabbabjhdultrx2uciy

Finding deterministic solution from underdetermined equation

Xin Li
2009 Proceedings of the 46th Annual Design Automation Conference on ZZZ - DAC '09  
Our goal is to solve a large number of (e.g., 10 4~1 0 6 ) model coefficients from a small set of (e.g., 10 2~1 0 3 ) sampling points without over-fitting.  ...  In this paper, we adapt a novel L 1 -norm regularization method to address this modeling challenge.  ...  Towards this goal, a two-step approach can be used: (a) solve the optimization in (11) for a set of different Ȝ's, and (b) select the optimal Ȝ by cross-validation.  ... 
doi:10.1145/1629911.1630009 dblp:conf/dac/Li09 fatcat:bzgb22gyh5dtxnhq7vgwx4g7bu

Optimization of Gaussian Random Fields [article]

Eric Dow, Qiqi Wang
2014 arXiv   pre-print
This sensitivity information is then incorporated into a gradient-based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics.  ...  This framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade.  ...  An efficient approach to solving (4.2) is the sequential quadratic programming method.  ... 
arXiv:1407.1857v1 fatcat:ao4we62pbbbdhpccws3o2pu52y

A Class of SDRE-RRT Based Kinodynamic Motion Planners

Adnan Tahirovic, Faris Janjos
2018 2018 Annual American Control Conference (ACC)  
By solving an LQR tracking problem for nonlinear systems within the SDRE framework, instead of a two point boundary value problem, the proposed planners deal with a wider range of controllable nonlinear  ...  A variety of LQR-RRT kinodynamic motion planners are built on the idea of solving a two point boundary value problem in an LQR manner for affine systems.  ...  However, using an infinitehorizon LQR controller to expand the tree from the nearest node toward a random sample is not optimal for finitetime extension even for linear systems.  ... 
doi:10.23919/acc.2018.8431412 dblp:conf/amcc/TahirovicJ18 fatcat:hwb7bv5cdvcgxkslqjcnb4es7e

Learning Large DAGs by Combining Continuous Optimization and Feedback Arc Set Heuristics [article]

Pierre Gillot, Pekka Parviainen
2021 arXiv   pre-print
We propose two scalable heuristics for learning DAGs in the linear structural equation case.  ...  Our methods learn the DAG by alternating between unconstrained gradient descent-based step to optimize an objective function and solving a maximum acyclic subgraph problem to enforce acyclicity.  ...  The authors thank Young Woong Park for providing the R code for GD.  ... 
arXiv:2107.00571v1 fatcat:4dkwpw7t5rakljrxtrg2ixl7z4

TGK-Planner: An Efficient Topology Guided Kinodynamic Planner for Autonomous Quadrotors [article]

Hongkai Ye, Xin Zhou, Zhepei Wang, Chao Xu, Jian Chu, Fei Gao
2020 arXiv   pre-print
The optimization program is formulated as a sequence of quadratic programmings (QPs) and can be iteratively solved in a few milliseconds.  ...  Firstly, we propose the topology guided graph, which roughly captures the topological structure of the environment and guides the state sampling of a sampling-based kinodynamic planner.  ...  Solving this equation along with the boundary and transversality conditions, we obtain the optimal solution pair {u * (t), p * (t)} which is: p * k (t) = 1 6 c k,3 t 3 + 1 2 c k,2 t 2 + c k,1 t + c k,0  ... 
arXiv:2008.03468v2 fatcat:lh3vum657rgd3e4idbdpptugqa
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