scholarly journals New gradient methods for sensor selection problems

2019 ◽  
Vol 15 (3) ◽  
pp. 155014771983964
Author(s):  
De Zhang ◽  
Mingqiang Li ◽  
Feng Zhang ◽  
Maojun Fan
Keyword(s):  
Optimization Problem ◽  
Gradient Methods ◽  
Sensor Selection ◽  
Selection Problem ◽  
Projected Gradient Method ◽  
Step Size ◽  
Convex Optimization Problem ◽  
Selection Problems ◽  
Combinational Optimization ◽  
Relaxed Problem

In this article, we consider the sensor selection problem of choosing [Formula: see text] sensors from a set of [Formula: see text] possible sensor measurements. The sensor selection problem is a combinational optimization problem. Evaluating the performance for each possible combination is impractical unless [Formula: see text] and [Formula: see text] are small. We relax the original selection problem to be a convex optimization problem and describe a projected gradient method with Barzilai–Borwein step size to solve the proposed relaxed problem. Numerical results demonstrate that the proposed algorithm converges faster than some classical algorithms. The solution obtained by the proposed algorithm is closer to the truth.

scholarly journals Inverse reinforcement learning in contextual MDPs

2021 ◽  
Author(s):  
Stav Belogolovsky ◽  
Philip Korsunsky ◽  
Shie Mannor ◽  
Chen Tessler ◽  
Tom Zahavy
Keyword(s):  
Reinforcement Learning ◽  
Optimization Problem ◽  
Decision Processes ◽  
Inverse Reinforcement Learning ◽  
Convex Optimization Problem ◽  
Reward Function ◽  
Dynamic Treatment Regime ◽  
Markov Decision ◽  
Dynamic Treatment ◽  
Recorded Data

AbstractWe consider the task of Inverse Reinforcement Learning in Contextual Markov Decision Processes (MDPs). In this setting, contexts, which define the reward and transition kernel, are sampled from a distribution. In addition, although the reward is a function of the context, it is not provided to the agent. Instead, the agent observes demonstrations from an optimal policy. The goal is to learn the reward mapping, such that the agent will act optimally even when encountering previously unseen contexts, also known as zero-shot transfer. We formulate this problem as a non-differential convex optimization problem and propose a novel algorithm to compute its subgradients. Based on this scheme, we analyze several methods both theoretically, where we compare the sample complexity and scalability, and empirically. Most importantly, we show both theoretically and empirically that our algorithms perform zero-shot transfer (generalize to new and unseen contexts). Specifically, we present empirical experiments in a dynamic treatment regime, where the goal is to learn a reward function which explains the behavior of expert physicians based on recorded data of them treating patients diagnosed with sepsis.

Extended state observer-based robust non-linear integral dynamic surface control for triaxial MEMS gyroscope

Robotica ◽  
2018 ◽  
Vol 37 (3) ◽  
pp. 481-501 ◽  
Author(s):  
Mehran Hosseini-Pishrobat ◽  
Jafar Keighobadi
Keyword(s):  
Optimization Problem ◽  
Dynamic Surface Control ◽  
Extended State ◽  
Gain Function ◽  
Dynamic Surface ◽  
Convex Optimization Problem ◽  
Mems Gyroscope ◽  
Surface Control ◽  
Non Linear ◽  
Linear Integral

SUMMARYThis paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$-robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ($\mathcal{L}_2$-$\mathcal{L}_\infty$) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$-$\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.

scholarly journals Shearlet-based regularized reconstruction in region-of-interest computed tomography

2018 ◽  
Vol 13 (4) ◽  
pp. 34
Author(s):  
T.A. Bubba ◽  
D. Labate ◽  
G. Zanghirati ◽  
S. Bonettini
Keyword(s):  
Optimization Problem ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Tomographic Reconstruction ◽  
Region Of Interest ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Convex Optimization Problem ◽  
Scanning Time ◽  
Novel Approach

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, bothad hocanalytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.

scholarly journals Low Complexity Sparse Beamspace DOA Estimation Via Single Measurement Vectors for Uniform Circular Array

2021 ◽  
Author(s):  
Di Zhao ◽  
Weijie Tan ◽  
Zhongliang Deng ◽  
Gang Li
Keyword(s):  
Optimization Problem ◽  
Signal To Noise Ratio ◽  
Estimation Method ◽  
Doa Estimation ◽  
Low Complexity ◽  
Estimation Methods ◽  
Circular Array ◽  
Single Measurement ◽  
Signal Model ◽  
Convex Optimization Problem

Abstract In this paper, we present a low complexity beamspace direction-of-arrival (DOA) estimation method for uniform circular array (UCA), which is based on the single measurement vectors (SMVs) via vectorization of sparse covariance matrix. In the proposed method, we rstly transform the signal model of UCA to that of virtual uniform linear array (ULA) in beamspace domain using the beamspace transformation (BT). Subsequently, by applying the vectorization operator on the virtual ULA-like array signal model, a new dimension-reduction array signal model consists of SMVs based on Khatri-Rao (KR) product is derived. And then, the DOA estimation is converted to the convex optimization problem. Finally, simulations are carried out to verify the eectiveness of the proposed method, the results show that without knowledge of the signal number, the proposed method not only has higher DOA resolution than subspace-based methods in low signal-to-noise ratio (SNR), but also has much lower computational complexity comparing other sparse-like DOA estimation methods.

scholarly journals Heliostat Field Layout Optimization with Evolutionary Algorithms

10.29007/7p6t ◽  
2018 ◽  
Author(s):  
Pascal Richter ◽  
David Laukamp ◽  
Levin Gerdes ◽  
Martin Frank ◽  
Erika Ábrahám
Keyword(s):  
Power Plant ◽  
Convex Optimization ◽  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Computer Science ◽  
Energy Supply ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
New Genotype

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant.We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals.Experimental results show the applicability of our approach.

scholarly journals A Dai-Liao Hybrid Hestenes-Stiefel and Fletcher-Revees Methods for Unconstrained Optimization

2021 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Nasiru Salihu ◽  
Mathew Remilekun Odekunle ◽  
Also Mohammed Saleh ◽  
Suraj Salihu
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Methods ◽  
Approximate Solutions ◽  
Step Size ◽  
Conjugacy Condition ◽  
Inexact Line Search ◽  
Wolfe Line Search

Some problems have no analytical solution or too difficult to solve by scientists, engineers, and mathematicians, so the development of numerical methods to obtain approximate solutions became necessary. Gradient methods are more efficient when the function to be minimized continuously in its first derivative. Therefore, this article presents a new hybrid Conjugate Gradient (CG) method to solve unconstrained optimization problems. The method requires the first-order derivatives but overcomes the steepest descent method’s shortcoming of slow convergence and needs not to save or compute the second-order derivatives needed by the Newton method. The CG update parameter is suggested from the Dai-Liao conjugacy condition as a convex combination of Hestenes-Stiefel and Fletcher-Revees algorithms by employing an optimal modulating choice parameterto avoid matrix storage. Numerical computation adopts an inexact line search to obtain the step-size that generates a decent property, showing that the algorithm is robust and efficient. The scheme converges globally under Wolfe line search, and it’s like is suitable in compressive sensing problems and M-tensor systems.

scholarly journals Learning Discriminative Correlation Subspace for Heterogeneous Domain Adaptation

2017 ◽  
Author(s):  
Yuguang Yan ◽  
Wen Li ◽  
Michael Ng ◽  
Mingkui Tan ◽  
Hanrui Wu ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Domain Adaptation ◽  
Data Sets ◽  
Target Domain ◽  
Real World Data ◽  
Discriminative Ability ◽  
Convex Optimization Problem ◽  
Alternating Direction ◽  
Feature Spaces ◽  
Target Data

Domain adaptation aims to reduce the effort on collecting and annotating target data by leveraging knowledge from a different source domain. The domain adaptation problem will become extremely challenging when the feature spaces of the source and target domains are different, which is also known as the heterogeneous domain adaptation (HDA) problem. In this paper, we propose a novel HDA method to find the optimal discriminative correlation subspace for the source and target data. The discriminative correlation subspace is inherited from the canonical correlation subspace between the source and target data, and is further optimized to maximize the discriminative ability for the target domain classifier. We formulate a joint objective in order to simultaneously learn the discriminative correlation subspace and the target domain classifier. We then apply an alternating direction method of multiplier (ADMM) algorithm to address the resulting non-convex optimization problem. Comprehensive experiments on two real-world data sets demonstrate the effectiveness of the proposed method compared to the state-of-the-art methods.

scholarly journals Reconstruction of the early Universe as a convex optimization problem

2003 ◽  
Vol 346 (2) ◽  
pp. 501-524 ◽  
Author(s):  
Y. Brenier ◽  
U. Frisch ◽  
M. Hénon ◽  
G. Loeper ◽  
S. Matarrese ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Early Universe ◽  
Optimization Problem ◽  
Convex Optimization Problem

Design of Low Order Controllers for Decoupled MIMO Systems With Time Response Specifications

2018 ◽  
pp. 90-128
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Mimo Systems ◽  
Design Method ◽  
Optimal Solution ◽  
Time Response ◽  
Convex Optimization Problem ◽  
Tito Systems ◽  
Low Order

The design of a low order controller for decoupled MIMO systems is proposed. The main objective of this controller is to guarantee some closed loop time response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a non-convex optimization problem. In order to obtain an optimal solution, the use of a global optimization method is suggested. In this chapter, the proposed solution is the GGP method. The principle of this method consists of transforming a non-convex optimization problem to a convex one by some mathematical transformations. So as to accomplish the fixed goal, it is imperative to decouple the coupled MIMO systems. To approve the controllers' design method, the synthesis of fixed low order controller for decoupled TITO systems is presented firstly. Then, this design method is generalized in the case of MIMO systems. Simulation results and a comparison study between the presented approach and a PI controller are given in order to show the efficiency of the proposed controller. It is remarkable that the obtained solution meets the desired closed loop time specifications for each system output. It is also noted that by considering the proposed approach the user can fix the desired closed loop performances for each output independently.

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